Foundation of Functions Worksheet

Problem 1 :

Domain: {x| x ≥ 0, x ≠ 2} Range: {y|-3 < y ≤ 3} Which graph corresponds to the given constraints?

Solution

Problem 2 :

Tyrone wants to spend at most $10,000 on two televisions, R and S. Each television must cost at least $3,000, and television R must cost at least twice as much as television S. Which system of inequalities models the amount of money spent on each television?

Solution

Problem 3 :

Meredith invests $50,000 in her new business. It costs the company $10 to produce each unit, which is sold for $15. Let C represent the cost and R represent the revenue for x units. Which statement is true about the graphs of the equations

C = 50,000 + 10x and R = 15x ?

A) Both slopes are positive.

B) Both slopes are negative.

C) One slope is positive, and the other is zero.

D) One slope is negative, and the other is positive.

Solution

Problem 4 :

Which graph represents the inverse of f(x) = 2x?

Solution

Problem 5 :

How many real roots does the function given by the graph have?

A. 0 real roots    B. 1 real root    C. 2 real roots

D. 4 real roots

Solution

Problem 6 :

What number is added to both sides of the equation

x² - 8x + 3 = 0

to solve it by completing the square?

A. -16      B. 16     C. -64      D. 64

Solution

Problem 7 :

What is the inverse of f(x) = x + 1?

A. f^-1(x) = -x - 1

B. f^-1(x) = x - 1

Solution

Problem 8 :

What is the inverse of the function f(x) = (x + 4)²?

Solution