3-2,3-3 Graphs and Properties of Functions TEAGUE Example 1) Find y when x is -14 Find y when x is -4 At x = 4 is the y value + or - At x = -4 is the y value + or - The intervals above the x-axis (-12,-2)(8, 12] Most left point and most right point Lowest and highest point Where the graph touches the x-axis and same as f(x) = 0 in part e -6 6 6 -3 -12<x<-2, 8<x12 -12, -2, 8 {x|-14x12} {y|-6y9} -12, -2, 8,
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3-2,3-3 Graphs and Properties of Functions TEAGUE · 3-2,3-3 Graphs and Properties of Functions TEAGUE Example 1) Find y when x is -14 Find y when x is -4 At x = 4 is the y value
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3-2,3-3 Graphs and Properties of Functions TEAGUE
Example 1)
Find y when x is -14
Find y when x is -4
At x = 4 is the y value + or -
At x = -4 is the y value + or -
The intervals above the x-axis
(-12,-2)(8, 12]
Most left point and most right point
Lowest and highest point
Where the graph touches the x-axis and same as f(x) = 0 in part e
-6
6
6
-3
-12<x<-2, 8<x12
-12, -2, 8
{x|-14x12}
{y|-6y9}
-12, -2, 8,
times
Where the graph touches the y-axis
If you draw a horizontal line at 1
If you draw a vertical line at
Give x where y is -6
Give x where y is 9
Example 2)
-3
3 times
1 times
x =-14, 4
- times
x = -6
times
Example 3)
from left to right from bottom to top
(-,5)
times
1
(0,3)
times
Example 4)
Example 5)
Is the point (2,11) on the graph?
Set the equation = -3 and get 4x2 – x=0
factor x(4x-1)=0
Factor the original to get x-intercepts (slide and divide)
(-,10]
times
(-,)
times
(10,0)(-15,0),(0,10)
15
(-2,15)
0,¼
(0,-3),( ¼,-3),
(-,)
times 1,¾ -3
Example 6) 𝒇(𝒙) =𝒙−𝟓
𝒙+𝟐 * domain set bottom = 0
a) Give the domain: {x|x≠-2} * x-intercepts set top = 0
b) Is the point (1,𝟑 𝟐⁄ ) on the graph of f? 𝟏−𝟓
𝟏+𝟐=
−𝟒
𝟑 NO, doesn’t = 3 2⁄
c) If x=2, what is f(x)? 𝟐−𝟓
𝟐+𝟐=
−𝟑
𝟒 List the point (2,
−3
4)
d) If f(x) = 2, what is x? x−5
x+2= 2
2x+4=x-5 x=-9 List the point (-9,2)
e) What are the x-intercepts? Set y=0 x−5
x+2= 0 x-5=0 x=5
don’t use the bottom bc it makes it undefined List the points (-5,0)
* to get the y-intercepts – just cover up the x values = −𝟓