Polynomials
Exponential Functions
Logarithmic Functions
Inverses
Solving Equations Exp/Log
100

Decide if the following are polynomials. If they are: state the degree. If they are not: say why not

f(x)= x2+3x5-7x3+ 𝝿 

g(x)=x3-21x2+3x+10

f(x): Yes! degree=5

g(x): No! Polynomials don't have variables in the exponent

100

Write the parent function for an exponential function with base 1/2 and graph it (label two points and any asymptotes)

f(x) = (1/2)x

H.A. y=0

100

Rewrite the following in logarithmic form

1331 = 113

log11(1331) = 3

100

How do you know if a function has an inverse by looking at the graph?

A function has an inverse if it passes the horizontal line test

100

Solve the following exponential equation for x:

3x+9 = 37x-6

x= 5/2

200

List all the possible rational roots of the following polynomial:

h(x) = 3x3 + 5x2 - x + 8

+-1, +-2, +-4, +-8, +-1/3, +-2/3, +-4/3, +-8/3

200

State the domain and range of 

g(x) = 5x+2 - 7

Domain: all real numbers

Range: (-7, infinity)

200
Simplify the following to a single logarithmic expression


log4(x) + log4(2x+1) - 3log4(y)


log4((2x2+x)/y3)

200

Find the inverse of 

f(x) = 3x + 12

f-1(x) = (1/3)x - 4

200

Solve the following logarithmic equation for x:

log7(2) + log7(x) = log7(3x-2)

x = 2

300

Let g(x) = x3. List all of the transformations applied to g(x) in order to obtain f(x) = -(2x+6)3-2

First rewrite as f(x) = -(2(x+3))-2

Horizontal shrink by a factor of 1/2, horizontal shift left by 3, reflect over the x-axis, vertical shift down 2.

300

Find the limit as x approaches infinity of f(x) and the limit as x approaches negative infinity of f(x) 

f(x) = (1/4)-x + 1

limit towards infinity: infinity 

limit towards negative infinity: 1

300

State the domain and range of the following:

f(x) = log9(3x+6) + 1


Domain: (-2, infinity)

Range: all real numbers

300

Find the range of the inverse of

f(x) = 5/(x - 4)

Range of f-1(x): (-infinity, 4) U (4, infinity) 

The range of f-1(x) is the domain of f(x)

300

Solve the following exponential equation for x:

43x+2 = 8x(43)

x = 2/3

400

Let f(x) = (x+2)(x-4)(3x+4)(2x-2)

Find the following:

-all the x-intercepts

-the degree of the polynomial

-the limit as x approaches infinity 

-the limit as x approaches negative infinity

x-intercepts: -2, 4, -4/3, 1

degree = 4

both limits go towards infinity

400

g(x) = 2(1/3)-x + 2

State the parent function, graph the parent function, then graph g(x) using transformations.

Parent function: f(x) = (1/3)x


400

g(x) = log3(x-1) + 2

State the parent function, graph the parent function, then graph g(x) using transformations.

Parent function: f(x) = log3(x)

400

Let f(x) = x2 + 3 

What is f-1(19) ?

f-1(19) = 4 because f(4) = 19

400

Solve the following logarithmic equation for x:

log5(6) + log5(2x2) = log5(96) - log5(2)

x = 2, -2

500

Fully factor the following polynomial using the rational root theorem and polynomial long division.

p(x) = x3 - 2x2 - 5x + 6

Possible rational roots: +-1, +-2, +-3, +-6

p(x) = (x-1)(x+2)(x-3)

500

Rewrite the following equation in the form f(x) = bx and state the value of b:

f(x) = (1/5)x(25)2x(125)x/3



f(x) = 625x

b=625

500

State the end-behaviors of the following logarithmic equation:

f(x) = log3(-x+2) - 5


limit as x approaches 2 from the left is negative infinity

limit as x approaches negative infinity is infinity

500

Find the inverse of 

f(x) = (2x+3)/(x-4)

f-1(x) = (3+4x)/(x-2)

500

Solve the following logarithmic equation for x:

log4(12+x) + log4(x) = 3

x = 4 

x = -16 is not included because it is outside of the domain

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