3.1 Assignment – Graphing Linear Functions & Quadratics in ...

Name _______________________________________________________ Date ___________________ Block _____

3.1 Assignment – Graphing Linear Functions & Quadratics in (ℎ, 𝑘)

Graph the following equations and answer the corresponding questions.

1. 𝑦 = −1

2𝑥 − 1 2. 3𝑥 − 4𝑦 = −12

Slope: _______ 𝑦-int: _______ Slope: _______ 𝑦-int: _______

Domain: _______ 𝑥-int: _______ Domain: _______ 𝑥-int: _______

Range: _______ Range: _______

3. 𝑦 = −(𝑥 + 3)2 + 16

Vertex: _______ 𝑎 is ______________ so the graph ________________________ 𝑦-int: _______ 𝑥-int(s): _______

Reflection of the 𝑦-int: _______ Axis of symmetry: _______

Extrema: _________________________________________

End Behavior: As 𝑥 → ∞ , 𝑦 → ___ As 𝑥 → −∞ , 𝑦 → ___

Increasing interval: _______ Decreasing interval: _______

Domain: ______________ Range: ______________

Transformations from the parent function (𝑦 = 𝑥2):

4. 𝑦 = 2𝑥2 − 50

Vertex: _______ 𝑎 is ______________ so the graph ________________________ 𝑦-int: _______ 𝑥-int(s): _______

Reflection of the 𝑦-int: _______ Axis of symmetry: _______

Extrema: _________________________________________

End Behavior: As 𝑥 → ∞ , 𝑦 → ___ As 𝑥 → −∞ , 𝑦 → ___

Increasing interval: _______ Decreasing interval: _______

Domain: ______________ Range: ______________

Transformations from the parent function (𝑦 = 𝑥2):

5. 𝑥 = 6 6. 𝑦 + 6 = 3

2 (𝑥 + 2)

Slope: _______ 𝑦-int: _______ Slope: _______ 𝑦-int: _______

Domain: _______ 𝑥-int: _______ Domain: _______ 𝑥-int: _______

Range: _______ Range: _______

7. 𝑔(𝑥) = −1

4(𝑥 + 2)2 + 4

Vertex: _______ 𝑎 is ______________ so the graph ________________________ 𝑦-int: _______ 𝑥-int(s): _______

Reflection of the 𝑦-int: _______ Axis of symmetry: _______

Extrema: _________________________________________

End Behavior: As 𝑥 → ∞ , 𝑦 → ___ As 𝑥 → −∞ , 𝑦 → ___

Increasing interval: _______ Decreasing interval: _______

Domain: ______________ Range: ______________

Transformations from the parent function (𝑦 = 𝑥2):

8. 𝑦 =1

2(𝑥 − 3)2 − 8

Vertex: _______ 𝑎 is ______________ so the graph ________________________ 𝑦-int: _______ 𝑥-int(s): _______

Reflection of the 𝑦-int: _______ Axis of symmetry: _______

Extrema: _________________________________________

End Behavior: As 𝑥 → ∞ , 𝑦 → ___ As 𝑥 → −∞ , 𝑦 → ___

Increasing interval: _______ Decreasing interval: _______

Domain: ______________ Range: ______________

Transformations from the parent function (𝑦 = 𝑥2):

Name _______________________________________________________ Date ___________________ Block _____

3.2 Assignment – Graphing Quadratic Equations in Standard Form

Graph the equations below and completely label the vertex, intercepts, and reflection of the y-intercept.

1. 𝑦 = 𝑥2 − 10𝑥 + 25

Vertex: _______ 𝑦-intercept: _______ 𝑥-intercept(s): _______ End Behavior: As 𝑥 → −∞, 𝑦 → ____

𝑎 is _________________ As 𝑥 → ∞, 𝑦 → ____

Refl. of 𝑦-int: _________

Axis of Symmetry: _______

D: _______ R: _______

Extrema: ______________

Transformations:

2. 𝑦 = −4𝑥2 + 8𝑥

Vertex: _______ 𝑦-intercept: _______ 𝑥-intercept(s): _______ End Behavior: As 𝑥 → −∞, 𝑦 → ____

𝑎 is _________________ As 𝑥 → ∞, 𝑦 → ____

Refl. of 𝑦-int: _________

Axis of Symmetry: _______

D: _______ R: _______

Extrema: ______________

Transformations:

3. ℎ(𝑥) = 9𝑥2 − 4

Vertex: _______ 𝑦-intercept: _______ 𝑥-intercept(s): _______ End Behavior: As 𝑥 → −∞, 𝑦 → ____

𝑎 is _________________ As 𝑥 → ∞, 𝑦 → ____

Refl. of 𝑦-int: _________

Axis of Symmetry: _______

D: _______ R: _______

Extrema: ______________

Transformations:

4. 3𝑥2 + 12𝑥 = 15

Vertex: _______ 𝑦-intercept: _______ 𝑥-intercept(s): _______ End Behavior: As 𝑥 → −∞, 𝑦 → ____

𝑎 is _________________ As 𝑥 → ∞, 𝑦 → ____

Refl. of 𝑦-int: _________

Axis of Symmetry: _______

D: _______ R: _______

Extrema: ______________

Transformations:

5. 𝑓(𝑥) = −𝑥2 − 8𝑥 − 16

Vertex: _______ 𝑦-intercept: _______ 𝑥-intercept(s): _______ End Behavior: As 𝑥 → −∞, 𝑦 → ____

𝑎 is _________________ As 𝑥 → ∞, 𝑦 → ____

Refl. of 𝑦-int: _________

Axis of Symmetry: _______

D: _______ R: _______

Extrema: ______________

Transformations:

Name _______________________________________________________ Date ___________________ Block _____

3.3 Assignment – Applications of Quadratic Equations

Answer each question, making sure to support your answers ALGEBRAICALLY, or NO CREDIT will be given.

1. A flare is launched from a boat. The height, ℎ, in meters of the flare above the water is approximately modeled by

the function ℎ(𝑡) = −15𝑡2 + 150𝑡 , where 𝑡 is the number of seconds after the flare is launched.

a) How long will the flare be in the air? Sketch:

b) At what time will the flare be at its maximum height?

c) What is the maximum height the flare will reach?

d) What is the height of the flare after 3.5 seconds? e) At what time(s) will the flare be at a height of 315 meters?

2. An osprey, a fish-eating bird of prey, dives towards the water to a salmon. The height, ℎ, in meters, of the osprey

above the water 𝑡 seconds after it begins its dive can be approximated by the function ℎ(𝑡) = 5𝑡2 − 30𝑡 + 45.

a) How long will it take the bird to get to the water to catch a salmon? Sketch:

b) What is the 𝑦-intercept and what does it mean in this situation?

c) What is the height of the osprey after 7 seconds? d) At what time(s) will the osprey be at a height of 45 meters?

3. Angela opened a surf shop in Southern California. Her accountant models her profit, 𝑃, in dollars with the function

𝑃(𝑡) = 1125𝑡2 − 2250𝑡 − 9000 where 𝑡 is the number of years in operation.

a) What is the 𝑦-intercept and what does it mean in this situation? Sketch:

b) How many years will it take for Angela to break even?

c) What is the vertex and what does it mean in this situation?

d) How long will it take for Angela to make more than $50, 000? Round to the nearest year.

e) How much profit will Angela make after 10 years?

Name ________________________________________________ Date _____________________ Block __________

3.4 Assignment – Graphing Square Root Functions

Graph the following functions and answer the corresponding questions.

1. 𝒚 = √𝒙 + 𝟑

(ℎ, 𝑘): _____ 𝑎 = _____ 𝑥-int: _____ 𝑦-int: _____ Three points on the graph: ______________________

D: __________ R: ________

Increasing: _______ Decreasing: _______

Transformations:

2. 𝒚 = 𝟐𝒙𝟐 + 𝟒𝒙 + 𝟐

Vertex: _______ 𝑦-int: _______ 𝑥-int(s): _______ 𝑎 is _________________ Reflection of 𝑦-int: _______

Axis of Symmetry: _______

Extrema: ______________

D: _______ R: _______

Increasing Interval: ______

Decreasing Interval: ______

End Behavior: As 𝑥 → −∞, 𝑦 → ____

As 𝑥 → ∞, 𝑦 → ____

Transformations:

3. 𝒚 = −√𝒙 + 𝟏

(ℎ, 𝑘): _____ 𝑎 = _____ 𝑥-int: _____ 𝑦-int: _____ Three points on the graph: ______________________

D: __________ R: ________

Increasing: _______ Decreasing: _______

Transformations:

4. 𝒚 = 𝟑𝒙𝟐 + 𝟔𝒙

Vertex: _______ 𝑦-int: _______ 𝑥-int(s): _______ 𝑎 is _________________ Reflection of 𝑦-int: _______

Axis of Symmetry: _______

Extrema: ______________

D: _______ R: _______

Increasing Interval: ______

Decreasing Interval: ______

End Behavior: As 𝑥 → −∞, 𝑦 → ____

As 𝑥 → ∞, 𝑦 → ____

Transformations:

5. 𝒚 = −𝟐(𝒙 + 𝟐)𝟐 + 𝟏𝟖

Vertex: _______ 𝑦-int: _______ 𝑥-int(s): _______ 𝑎 is _________________ Reflection of 𝑦-int: _______

Axis of Symmetry: _______

Extrema: ______________

D: _______ R: _______

Increasing Interval: ______

Decreasing Interval: ______

End Behavior: As 𝑥 → −∞, 𝑦 → ____

As 𝑥 → ∞, 𝑦 → ____

Transformations:

6. 𝒚 = 𝟐√𝒙

(ℎ, 𝑘): _____ 𝑎 = _____ 𝑥-int: _____ 𝑦-int: _____ Three points on the graph: ______________________

D: __________ R: ________

Increasing: _______ Decreasing: _______

Transformations:

Name _______________________________________________________ Date ___________________ Block _____

3.5 Assignment – Graphing Polynomial Functions

Using a graphing utility, answer the questions for each polynomial and sketch the graph. Label all points.

1. 𝑦 = 6𝑥4 − 𝑥3 − 9𝑥2 − 2𝑥 − 2 𝑎 is ______________ The equation is even / odd Same / Opposite end behavior

𝑥-int: ______________________________________ 𝑦-int: _______

As 𝑥 → −∞ , 𝑦 → _____ As 𝑥 → ∞, 𝑦 → _____

Increasing interval: ___________________________

Decreasing interval: ___________________________

Minimum / Maximum:

___________________________________________

___________________________________________

2. ℎ(𝑥) = −3𝑥3 + 3𝑥 − 1 𝑎 is ______________ The equation is even / odd Same / Opposite end behavior

𝑥-int: ______________________________________ 𝑦-int: _______

As 𝑥 → −∞ , 𝑦 → _____ As 𝑥 → ∞, 𝑦 → _____

Increasing interval: ___________________________

Decreasing interval: ___________________________

Minimum / Maximum:

___________________________________________

___________________________________________

3. 𝑓(𝑥) = 𝑥7 + 𝑥6 − 3𝑥5 + 5𝑥3 − 𝑥 + 2

𝑎 is ______________ The equation is even / odd Same / Opposite end behavior

𝑥-int: ______________________________________ 𝑦-int: _______

As 𝑥 → −∞ , 𝑦 → _____ As 𝑥 → ∞, 𝑦 → _____

Increasing interval: ___________________________

Decreasing interval: ___________________________

Minimum / Maximum:

___________________________________________

___________________________________________

Name ___________________________________________________ Date ___________________ Block _________

3.6 Assignment – Graphing Rational Functions

Match the following graphs with the given functions:

1. 𝑦 = 2

𝑥+3 _____ 2. 𝑦 =

1

𝑥−3 _____ 3. 𝑦 =

𝑥−1

𝑥−4 _____ 4. 𝑦 =

−𝑥−2

𝑥+4 _____

A. B. C. D.

Match the following graphs with the given functions:

5. 𝑦 = 5𝑥

𝑥−1 _____ 6. 𝑦 =

3𝑥2

𝑥2−1 _____ 7. 𝑦 =

1

𝑥−1 _____ 8. 𝑦 =

4𝑥

𝑥2−1 _____

A. B. C. D.

Find the discontinuity & axes intercepts in order to sketch each graph. Then, answer the remaining questions.

9. 𝑓(𝑥) = 2𝑥−1

𝑥 a) H.A.: _______ b) V.A.: _______ c) Hole: _______

Extrema: _____________________ 𝑥-intercept(s): ______ 𝑦-intercept: _______

Intervals of Increase: ___________

Intervals of Decrease: __________

As 𝑥 → −∞, 𝑦 → _____

As 𝑥 → ∞, 𝑦 → _____

Domain: _______ Range: _______

10. 𝑔(𝑥) = 𝑥

𝑥2−𝑥−2 =

𝑥

(𝑥−2)(𝑥+1) a) H.A.: _______ b) V.A.: _______ c) Hole: _______

Extrema: _____________________ 𝑥-intercept(s): ______ 𝑦-intercept: _______

Intervals of Increase: ___________

Intervals of Decrease: __________

As 𝑥 → −∞, 𝑦 → _____

As 𝑥 → ∞, 𝑦 → _____

Domain: _______ Range: _______

11. 𝑦 = 4

𝑥2−4 =

4

(𝑥+2)(𝑥−2) a) H.A.: _______ b) V.A.: _______ c) Hole: _______

Extrema: _____________________ 𝑥-intercept(s): ______ 𝑦-intercept: _______

Intervals of Increase: ___________

Intervals of Decrease: __________

As 𝑥 → −∞, 𝑦 → _____

As 𝑥 → ∞, 𝑦 → _____

Domain: _______ Range: _______

12. ℎ(𝑥) = 𝑥2−2𝑥−3

𝑥−3 =

(𝑥−3)(𝑥+1)

𝑥−3 a) H.A.: _______ b) V.A.: _______ c) Hole: _______

Extrema: _____________________ 𝑥-intercept(s): ______ 𝑦-intercept: _______

Intervals of Increase: ___________

Intervals of Decrease: __________

As 𝑥 → −∞, 𝑦 → _____

As 𝑥 → ∞, 𝑦 → _____

Domain: _______ Range: _______

13. 𝑓(𝑥) = 𝑥2−9

2𝑥2−6𝑥 =

(𝑥+3)(𝑥−3)

2𝑥(𝑥−3) a) H.A.: _______ b) V.A.: _______ c) Hole: _______

Extrema: _____________________ 𝑥-intercept(s): ______ 𝑦-intercept: _______

Intervals of Increase: ___________

Intervals of Decrease: __________

As 𝑥 → −∞, 𝑦 → _____

As 𝑥 → ∞, 𝑦 → _____

Domain: _______ Range: _______

Name ___________________________________________________ Date _____________________ Block _______

3.7 Assignment – Graphing Rational Functions with Slant Asymptotes

Divide using polynomial division.

1. 2𝑥3+7𝑥2+2𝑥+9

2𝑥+3 2. (𝑥3 − 12𝑥2 − 42) ÷ (𝑥2 − 2𝑥 + 1)

Provide the information and sketch the graph, labeling the discontinuity and axes intercepts.

3. 𝑦 = 2𝑥3+5𝑥2−6𝑥−9

𝑥2+𝑥−6 =

(𝑥+3)(2𝑥−3)(𝑥+1)

(𝑥+3)(𝑥−2) a) H.A.: _______ b) V.A.: _______ c) S.A. ______________

Hole: _______ 𝑥-intercept(s): ______

𝑦-intercept: _______

Extrema: _____________________

Int. of Inc: ______________

Int. of Dec.: ______________

As 𝑥 → −∞, 𝑦 → _____

As 𝑥 → ∞, 𝑦 → _____

Domain: _______

Range: _______

Provide the information and sketch the function, labelling the axes intercepts.

4. ℎ(𝑥) = 2𝑥2 + 4𝑥 − 70 Vertex: _______ 𝑦-int: _______ 𝑥-int(s): _______ 𝑎 is _________________

Reflection of 𝑦-int: _______

Axis of Symmetry: _______

Extrema: ______________

D: _______ R: _______

Increasing Interval: ______

Decreasing Interval: ______

End Behavior: As 𝑥 → −∞, 𝑦 → ____

As 𝑥 → ∞, 𝑦 → ____

Transformations:

5. 𝑦 = −√𝑥 − 1 + 3 (ℎ, 𝑘): _____ 𝑎 = _____ 𝑥-int: _____ 𝑦-int: _____

Three points on the graph: ______________________

D: __________ R: ________

Increasing: _______ Decreasing: _______

Transformations:

6. 𝑦 = 2𝑥2+4𝑥−6

𝑥2−16 =

2(𝑥+3)(𝑥−1)

(𝑥+4)(𝑥−4) a) H.A.: _______ b) V.A.: _______ c) S.A. ______________

Hole: _______ 𝑥-intercept(s): ______

𝑦-intercept: _______

Extrema: _____________________

Int. of Inc: ______________

Int. of Dec.: ______________

As 𝑥 → −∞, 𝑦 → _____

As 𝑥 → ∞, 𝑦 → _____

Domain: _______

Range: _______

Name _________________________________________ Date ______________________ Block _______

Unit 3 Think Piece

Graph the following Piecewise Functions.

1. 𝑓(𝑥) = 𝑓(𝑥) = {−

1

2𝑥 + 2, 𝑥 < 2

1, 𝑥 ≥ 2 2. 𝑓(𝑥) = {

(𝑥 + 3)2 − 1, 𝑥 ≤ −32

3𝑥 + 1, 𝑥 > −3

3. 𝑓(𝑥) = {−2𝑥 + 3, 𝑥 < 22𝑥 − 5. 𝑥 ≥ 2

4. 𝑓(𝑥) = {−1, 𝑥 < 3

√𝑥 − 3 − 1, 𝑥 ≥ 3

5. 𝑓(𝑥) = {3, 𝑥 ≤ 4

−(𝑥 − 4)2 + 3, 𝑥 > 4 6. 𝑓(𝑥) = {

(𝑥 + 2)2 + 1, 𝑥 < −2

√𝑥 + 2 + 1, 𝑥 ≥ −2

7. 𝑓(𝑥) = {𝑥 + 5, 𝑥 < −1 −3𝑥 + 1, 𝑥 ≥ −1

8. 𝑓(𝑥) = {−2, 𝑥 ≤ −2 1

2𝑥 − 1, 𝑥 > −2

Name ___________________________________________________ Date _____________________ Block _______

Algebra 3 – Unit 3 Test Review

1. Given the equation 𝑓(𝑥) = −3(𝑥 + 1)2 + 12:

a) What is the vertex? b) What is the 𝑦-intercept? c) What are the 𝑥-intercepts?

d) What is the domain? e) What is the range? f) As 𝑥 → −∞, 𝑦 → ____

As 𝑥 → ∞, 𝑦 → ____

g) Describe the transformations from the parent function 𝑦 = 𝑥2.

h) What is the axis of symmetry? i) Sketch the graph.

2. a) Write the function that transforms the parent function 𝑦 = √𝑥 four units to the right, reflected over the 𝑥-axis,

and one unit up.

b) Give three points on the graph using the table to the right c) Sketch the transformed graph.

3. Given the function 𝑦 = 2𝑥2 + 12𝑥 + 13

a) Find the vertex. b) Give the domain and range:

Domain: _______ Range: _______

4. Given the function 𝑦 = 𝑥2 − 2𝑥 − 15

a) What is the vertex? b) What is the axis of symmetry? c) As 𝑥 → −∞, 𝑦 → ____

As 𝑥 → ∞, 𝑦 → ____

𝑥 𝑦

5. Given the function 𝑦 = 3𝑥2 − 6𝑥 + 1

a) Find the vertex. b) Give the increasing and decreasing intervals:

Increasing: ______________

Decreasing: ______________

6. Graph the piecewise functions below:

a) 𝑓(𝑥) = {2𝑥 − 1 , 𝑖𝑓 𝑥 < 1𝑥 , 𝑖𝑓 𝑥 ≥ 1

b) 𝑔(𝑥) = {−4 , 𝑖𝑓 𝑥 ≥ −2 3

2𝑥 − 1 , 𝑖𝑓 𝑥 < −2

7. Given the function 𝑦 = 4𝑥3 − 5𝑥2 + 8 , use the graphing calculator to find the following:

a) 𝑥-intercept(s): _____________________ b) 𝑦-intercept: _______

c) Extema: ___________________________________ d) Domain: ______________

__________________________________________ Range: ____________

e) Intervals of increase: ________________________ f) Intervals of decrease: _________________________

g) As 𝑥 → −∞, 𝑦 → ____ As 𝑥 → ∞, 𝑦 → ____

8. Given the function 𝑓(𝑥) = −2𝑥3 − 7𝑥2 − 4𝑥 , use the graphing calculator to find the following:

a) 𝑥-intercept(s): _____________________ b) 𝑦-intercept: _______

c) Extema: ___________________________________ d) Domain: ______________

__________________________________________ Range: ____________

e) Intervals of increase: ________________________ f) Intervals of decrease: _________________________

g) As 𝑥 → −∞, 𝑦 → ____ As 𝑥 → ∞, 𝑦 → ____

9. 𝑔(𝑥) = 𝑥3+3𝑥2−4𝑥−12

𝑥2−𝑥−12 =

(𝑥+2)(𝑥−2)(𝑥+3)

(𝑥+3)(𝑥−4)

(a) Hole: _______ (b) Vertical Asymptote(s): _______

Work (if none, explain why) Work (if none, explain why)

(c) Horizontal Asymptote: _______ (d) Slant Asymptote: _______

Work (if none, explain why) Work (if none, explain why)

(e) 𝑥-intercept(s): _______

(f) 𝑦-intercept: _______

(g) Sketch the graph.

Label any intercepts, holes, and/or asymptotes.

(h) Extrema: _________________________________

(i) Intervals of increase: ________________________

(j) Intervals of decrease: _______________________

(k) As 𝑥 → −∞, 𝑦 → ______ As 𝑥 → ∞, 𝑦 → _______

(l) Domain: __________________________________

(m) Range: __________________________________

10. The height of a javelin in feet is modeled by the equation ℎ(𝑡) = −6𝑡2 + 29𝑡 + 5 where 𝑡 represents time in

seconds after the javelin is thrown.

a) Sketch the situation. Be sure to label the axes and any points you find.

b) How long is the javelin in the air? Support your answer algebraically.

c) At what time is the javelin at its maximum height? Support your answer algebraically.

d) What is the maximum height that the javelin reaches? Support your answer algebraically.

e) What is the height of the javelin after 1.5 seconds? Support your answer algebraically.

f) At what time(s) is the javelin at a height of 25 feet? Support your answer algebraically.

Name ____________________________________________________ Date ___________________ Block ________

4.1 Assignment – Exponential Growth Model

Use the exponential equation 𝒚 = 𝟑𝒙−𝟒 − 𝟐 to answer questions 1 – 5.

1. The transformations from the parent function are _______________________________________________________

2. The asymptote is _____________________

3. The domain is _____________________ and the range is _____________________

4. As 𝑥 → −∞, 𝑦 → As 𝑥 → ∞, 𝑦 →

5. The increasing interval is ______________. The decreasing interval is ______________.

Describe the transformation from the graph of the parent function. Sketch the graph, find and label two significant

points, and label the asymptote with its equation. SHOW ALL WORK.

6. 𝑓(𝑥) = 3𝑥+2 − 4

Transformations: ___________________________________________________________________________________

Significant Points: ______________ Asymptote: ______________

7. 𝑦 = 3(2)𝑥 + 8

Transformations: ___________________________________________________________________________________

Significant Points: ______________ Asymptote: ______________

8. 𝑔(𝑥) = 0.25(4)𝑥 − 6

Transformations: ___________________________________________________________________________________

Significant Points: ______________ Asymptote: ______________

Use the graph of 𝒇(𝒙) to the right to describe and sketch the transformations. Label the points with their

coordinates and the asymptote with its equation. SHOW ALL WORK.

(4, 22)

(−2, −2)

9. 𝑓(𝑥 − 2) 10. 𝑓(2𝑥) − 3

Transformations: ___________________________ Transformations: ___________________________

_________________________________________ _________________________________________

𝑦 = −4

Name ____________________________________________________ Date ___________________ Block ________

4.2 Assignment – Exponential Decay Model

Describe the transformation from the graph of the parent function. Sketch the graph, find and label two significant

points, and label the asymptote with its equation. SHOW ALL WORK.

1. 𝑦 = 5𝑥 Transformations: __________________________________________________

Significant Points: ______________ Asymptote: _______________

Domain: ______________

Range: ______________

Increasing: ______________

Decreasing: ______________

2. 𝑓(𝑥) = 1

8(

1

4)

𝑥+6

+7 Transformations: __________________________________________________

Significant Points: ______________ Asymptote: _______________

Domain: ______________

Range: ______________

Increasing: ______________

Decreasing: ______________

3. 𝑔(𝑥) = 3 (2

5)

1

2𝑥

– 6 Transformations: __________________________________________________

Significant Points: ______________ Asymptote: _______________

Domain: ______________

Range: ______________

Increasing: ______________

Decreasing: ______________

4. 𝑦 = 32𝑥 + 1 Transformations: __________________________________________________

Significant Points: ______________ Asymptote: _______________

Domain: ______________

Range: ______________

Increasing: ______________

Decreasing: ______________

For problems 5 & 6, describe and sketch the transformations of the graph. Label the significant points with their

ordered pairs and the asymptote with its equation.

5. 3𝑓(𝑥 − 2)

Transformations: (3, 6)

_____________________________ (−3, 1)

_____________________________ 𝑦 = −1

Significant Points: ______________

Asymptote: ______________

6. 𝑓(2𝑥)

Transformations:

_____________________________

_____________________________ (−4, −2) (1, −4)

Significant Points: ______________ 𝑦 = −6

Asymptote: ______________

7. If an amount of $5,000 is deposited into a savings account at an annual interest rate of 5%, compounded monthly,

what would be the value of the investment after 10 years?

8. If you start a bank account with $10,000 and your bank compounds the interest quarterly at an interest rate of 8%,

how much money do you have at the year's end? (assume that you do not add or withdraw any money from the

account)

Name ___________________________________________________ Date ___________________ Block _________

4.3 Assignment – Natural Growth & Decay Model

Describe the transformation(s) from the graph of the parent function. Sketch the graph, find and label two significant

points, and label the asymptote with its equation. SHOW ALL WORK.

1. 𝑓(𝑥) = 2 (1

3)

𝑥+1− 7 Transformations: __________________________________________________

Significant Points: ______________ Asymptote: _______________

Domain: ______________

Range: ______________

Increasing: ______________

Decreasing: ______________

As 𝑥 → −∞, 𝑦 → ____ As 𝑥 → ∞, 𝑦 → ____

2. 𝑔(𝑥) = 3𝑒𝑥 + 2 Transformations: __________________________________________________

Significant Points: ______________ Asymptote: _______________

Domain: ______________

Range: ______________

Increasing: ______________

Decreasing: ______________

As 𝑥 → −∞, 𝑦 → ____ As 𝑥 → ∞, 𝑦 → ____

3. 𝑦 = 22𝑥 Transformations: __________________________________________________

Significant Points: ______________ Asymptote: _______________

Domain: ______________

Range: ______________

Increasing: ______________

Decreasing: ______________

As 𝑥 → −∞, 𝑦 → ____ As 𝑥 → ∞, 𝑦 → ____

4. ℎ(𝑥) = 𝑒−4𝑥 − 1 Transformations: __________________________________________________

Significant Points: ______________ Asymptote: _______________

Domain: ______________

Range: ______________

Increasing: ______________

Decreasing: ______________

As 𝑥 → −∞, 𝑦 → ____ As 𝑥 → ∞, 𝑦 → ____

5. If you deposit $100 into a savings account which earns a 5% yearly interest rate, how much is in your account after

two years?

6. If you invest $500 at an annual interest rate of 10% compounded continuously, calculate the final amount you will

have in the account after five years.

7. If you invest $2,000 at an annual interest rate of 13% compounded continuously, calculate the final amount you will

have in the account after 20 years.

8. A first saving account pays 5% compounded annually. A second saving account pays 5% compounded continuously.

Which of the two investments is better in the long term? (Choose an amount for the principal and a period of time in

order to prove your answer).