$$I = 1000 \times 0.04 \times 3 = 120$$

Question 1

Which of the following represents the interval notation for the inequality $$x \u003e 3$$?

Accepted Answer

$$(3, \infty)$$

Question 2

A company models its profit $$P as a $$function of time $$t$$ using $$P(t) = 500e$$^{0.05t}$$. What type of function is this?

Accepted Answer

Exponential function

Question 3

Given the function $$f(x) = 2x + 5$$, what is the slope of the function?

Accepted Answer

$$2$$

Question 4

If the quadratic function $$f(x) = ax^2$ + bx + c$$ has its vertex at $$(h, k)$$, which formula gives the $$x-$$coordinate of the vertex?

Accepted Answer

$$h = -\frac{b}{2a}$$

Question 5

Which transformation describes the function $$g(x) = f(x) + 4$$ compared to $$f(x)$$?

Accepted Answer

Vertical translation up by 4 units

Question 6

A rectangle has length $$L = 8$$ and width $$W = 5. $$What is its perimeter?

Accepted Answer

$$P = 2L + 2W = 26$$

Question 7

Which of the following is the correct interval notation for $$a \u003c x \u003c b$$?

Accepted Answer

$$(a, b)$$

Question 8

If $$y$$ varies inversely with $$x$$, which equation best represents this relationship?

Accepted Answer

$$y = \frac{k}{x}$$

Question 9

A bank offers simple interest. If you invest $$P = 1000$$ dollars at a rate $$R = 0.04$$ for $$T = 3$$ years, what is the interest earned?

Accepted Answer

$$I = 1000 	imes 0.04 	imes 3 = 120$$

Question 10

Which formula is used to find the distance traveled if rate $$R$$ and time $$T$$ are known?

Accepted Answer

$$D = R 	imes T$$

Question 11

What is the solution to the equation $$2x - 5 = 9$$?

Accepted Answer

$$x = 7$$

Question 12

Which of the following is the correct formula for the quadratic formula?

Accepted Answer

$$x = \frac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$

Question 13

If $$f(x) = x^2$ and g(x) = 3x + 1$, what is (f$$ \circ g)(x)$$?

Accepted Answer

$$f(g(x)) = (3x + 1)^2$

Question 14

Which property of logarithms allows you to write $$\log_b(MN) = \log_b M + \log_b N$$?

Accepted Answer

Product Property

Question 15

A quadratic function $$f(x) = ax^2$ + bx + c$$ opens upward if:

Accepted Answer

$$a \u003e 0$$

Question 16

Which formula represents the area of a rectangle?

Accepted Answer

$$A = L 	imes W$$

Question 17

If $$f(x) = x^2$ is reflected in the x$-axis, what is the new function?

Accepted Answer

$$f(x) = -x^2$

Question 18

Which of the following is the correct interval notation for $$x is $$between $$a$$ and $$b$$, including both $$a$$ and $$b$$?

Accepted Answer

$$[a, b]$$

Question 19

If $$y$$ varies jointly with $$x$$ and $$z$$, which equation best represents this relationship?

Accepted Answer

$$y = kxz$$

College Algebra Essentials: Functions, Equations, and Notation

Study Guide - Practice Questions