Solving for Types of Functions

Absolute Value Functions

100

Which way is the function f(x)= -2|x+2|-3 facing? 

It is facing down since 2 is negative

200

What is the vertex of the function f(x) = -2|x+2|-3 ?

(-2, -3)

300

Solve for the function when x = -12

f(x)= 5|2x+10|-3 

67

400

Graph how the function f(x)= 3|x+7|+3

Vertex at (-7,3), slope is 3/1 facing up

500

Create an absolute value function equation that has a vertex at (-2, 6) and crosses (0,10). 

2|x+2|+6

Linear Functions

100

Solve the function when x=3

f(x)= 5x+10

f(3)=25

200

Create the equation: 

An engineer charges you $150 for the service and $25 for every hour they are working on your car. 

f(x)= 150 + 25x

300

Solve for the function f(7)= 32x -17

207

400

What is x when the function f(x) = 45x-22 is equal to 248

6

500

A lawyer charges $1250 an hour and has a one time charge of $725 to apply for his services. If the lawyer worked with you for 3 hours on Monday, Wednesday and Friday. Create an equation to represent this and how much do you owe her?

f(9) = 1250x +750 = $11, 975

Exponential Functions

100

If you have $1,000 in your bank account and it increases by 10 percent every year. If you on't add or withdraw any money, how much will you have in 2 years?

$1,210

200

What is f(3)= 2(8^x)

1024

300

What is the rate of change?

x     :   0      2      3      4      

f(x) :   6      24    48    96

times 2

400

A type of bacteria triples its cells every minute. If it started out with one bacteria, how many cells would there be in 10 minutes?

59,049 bacteria cells

500

The Flash was running at an exponential rate. He starts running at 25 miles per hour and triples every second. How many seconds until his speed is over 1 million?

Between 15 and 16 seconds. ~15.29 seconds

25(2¹⁵) = 819200

25(2¹⁶) = 1638400

Quadratic Functions

100

Solve by factoring:

x²+2x+3

(x+2)(x+1)

x= -2, -1

200

What are the solutions for the function 

f(x)= x^2+7x+10

x=5

x=2

300

Find the y intercept of the function:

f(x) = x^2+5x+138

(0,138)

400

Solve using the quadratic formula:

f(x)= 4x^2+8x-12

x= 3

x=-1

500

Solve by Completing the square:

f(x)= x^2 +7x-12

x= -7/2

x=-97/4

Roots Functions

100

What is the vertex of the function:

f(x)= sqr(x-1)

(1,0)

200

What is the solution for the function: 

f(x) = sqr(2x-1)

x= 1/2

(1/2,0)

300

What is the domain and range for a the function

f(x)= x^1/3

All real number for domain and range

400

Why is it possible to have cbrt(-1) but not sqrt(-1)?

Because you can cube root a negative number. You cannot square root a negative number. 

500

For what value does f(x) = 7 in the function 

f(x)= cbrt(x+4)-3

x=996