Review for Midterm 2 testaliacriddlemaw2010-2011portfolio.weebly.com/uploads/4/9/... · 2018. 9. 6. · Objectives Section 6.2 Section 6.2 Determine whether a function is one-to-one.

Test Instructions

Objectives Section 5.1

Section 5.1

Determine if a function is a polynomial function. State the degree of a

polynomial function.

Form a polynomial whose zeros and degree are given.

Graph transformations (vertical shifts, horizontal shifts, and reflections) of

power functions.

Find the zeros and multiplicities of a polynomial function and use them to Find the zeros and multiplicities of a polynomial function and use them to

determine whether the graph crosses or touches at each x-intercept.

Remember that zeros are the x-coordinates of the x-intercepts. Find the y-

intercept. Be able to state the power function that f resembles for large values

of |x| and state the maximum number of turning points. Determine the

behavior of the graph near the x-intercepts. Graph the function.

Review Problem Section 5.1

Fall 2006 Final Exam

Determine the maximum number of turning points on

the graph of f(x).the graph of f(x).

Determine the behavior of the graph of f near each x-

intercept.


Section 5.2

Find the domain of a rational function.

Find vertical and horizontal or oblique asymptotes



Finding Asymptotes pg 351




Section 5.3

Graph a rational function by analyzing the function: Find the domain, any

asymptotes, any intercepts, and sketch the graph.

Given the graph of a rational function, find the domain and range, any

intercepts, and any asymptotes.

Use your graphing calculator to find the approximate maximum value of a

function in an applied (word) problem.




Section 5.4

Solve rational and polynomial inequalities.





Objectives Section R.6

Section R.6

Use synthetic division to find the quotient and remainder.

Use synthetic division to determine whether x-c is a factor of f(x).

Review Problem Section R.6/Ch 6



Section 5.5

Use the Factor Theorem to determine whether x-c is a factor of f(x).

Know the maximum number of zeros a polynomial may have.

List the potential rational zeros of a polynomial function. (Use the Rational

Zeros Theorem.)

Use the above information to find the real zeros of a polynomial function and

write the function in factored form.write the function in factored form.

Solve polynomial equations in the real number system by using the above

information.




Section 5.6

Given the degree and some zeros of a polynomial with real coefficients, find the

remaining complex zeros.

Form a polynomial f(x) having given degree and complex zeros.

Find the complex zeros of a polynomial function and write the function in

factored form.






Section 6.1

Find the composite of two functions at a given value of x.

Find the composite of two functions and the domain of the composite function.




Section 6.2

Determine whether a function is one-to-one.

Determine if two functions f and g are inverses of each other.

Find the inverse of a function and state the domain and range of both

and .

( )f x1( )f x

−






Section 6.3 Graph without using a calculator in this section!

Graph an exponential function and transformations of .

State the domain, range, and horizontal asymptote.

Solve exponential equations by using: If then . u v

a a= u v=

( ) xf x a=( ) x

f x a=






Section 6.4 Graph without using a calculator in this section!

Change between exponential and logarithmic form of an equation.

Find the exact value of a logarithm.

Find the domain of a logarithmic function.

Graph , , and transformations of each. State the domain,

range, and vertical asymptote.

loga

y x= ln( )y x=

Solve logarithmic equations by changing to exponential form.




Section 6.5

Write an expression as a sum and/or difference of logarithms. Express powers

as factors.

Write an expression as a single logarithm.




Section 6.6

Solve logarithmic and exponential equations. Be able to give the exact solution.

Remember to check that solutions to logarithmic equations are in the domain.




Section 6.7

Solve application problems involving compound interest. You will need a

calculator.






Section 6.8

Solve application problems involving exponential growth and decay. Know how

to find or use half-life of a substance in solving problems. You will need a

calculator.


Final Exam Fall 2007


Final Exam Fall 2006

Review for Midterm 2 testaliacriddlemaw2010-2011portfolio.weebly.com/uploads/4/9/... · 2018. 9. 6. · Objectives Section 6.2 Section 6.2 Determine whether a function is one-to-one.

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