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Functions
Systems of Equations
Graphing
Inverses
Logarithms
100

f(x)=-4x-10

What is f(3)?

-22

100

To solve a system of 3 variables, how many distinct equations do you need?

3

100
At what point do the lines intersect?

y=3x+6

y+2x=-9

(-3, -3)

100

What is an inverse?

Sample responses: It's when the input and output are exchanged.

A function that maps the output back to the input.

The 'opposite' of a function.

100

Evaluate

log5125

3

200

f(x)=(8-x)2

What is f(11)?

f(11)=9
200

Solve by substitution. Express your answer as "x=_ y = _"

x=5

y=x+11

x=5
y=16

200

What does the graph of a LOGARITHMIC function look like?

Sample answer: It starts at the y-axis at negative infinity, and increases indefinitely by increments of less and less.

200

How do you find the inverse?

(Write the function in terms of y), switch x and y, and solve for y.

200

Evaluate.  Round to the nearest hundredth.

log8175

2.48

300

What is the standard form for the polynomial function:

f(x)=8x2 - 5x3 + 2 - 10x?

f(x) = -5x3 + 8x2 - 10x + 2

300

To solve a system by graphing, you graph both equations.  How do you find the solution?

The solution is where the two lines cross.

300

How do the graph of a function and its inverse relate?

The graph of the inverse is a reflection of the function (over the line y=x).

300

What is the inverse of

f(x)=x+9

f-1(x)=x-9

300
Evaluate.  Round to the nearest hundredth.

log25000

4.40

400

A small business has 15 customers.  The owner sets a goal to grow her business by 20% per year.  How many customers will she have in 5 years? (Round to the nearest whole number)

37 customers

400

Solve by substitution.

2x-5=y-13

y = 10x

x=1,y=10

400

Is there a solution to the system of equations:

y = 9x - 4

18x-2y = 0

Why or why not?

Sample response:

No, because the lines are parallel and never intersect, therefore there is no solution.

400

What is the inverse of

f(x)=2x - 18

f-1(x) = x/2 + 9

or 

f-1(x) = (x+18)/2

400

Solve the logarithmic equation:

log (x+3)= log24

x=21

500

Does the function f(x) = x4 have an inverse (that is a function)?  Why or why not?

Sample response: No, f(x) = x4 does not pass the horizontal line test, therefore its inverse does not pass the vertical line test, therefore its inverse is not a function.

500
The sum of two numbers is 44.  Their difference is 8.


What are the two numbers?

18 and 26

500

A car depreciates in value 16% per year.  Gus bought the car in 2020 for $34,000.  How much will it be worth in 2045? (Round to dollars and cents)

$434.97

500

What is f-1(6) according to the table below?

x          f(x)

2         8

3         6

4         3

5         0

6         -4

f-1(6)=3
500

Solve the logarithmic equation:

log6(8x)=3

x=27