Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{x-3}$$?

Accepted Answer

$$x \geq 3$$

Question 2

Given the function $$f(x) = 2x^2$ - 5x + 3$$, what is the vertex of its graph?

Accepted Answer

$$(1.25, 0.875)$$

Question 3

Which of the following is the correct composition of the functions $$f(x) = x^2$ and g(x) = x+1$ evaluated at x=2$ for f(g(x$$))$$?

Accepted Answer

$$9$$

Question 4

A population of bacteria doubles every 3 hours. If the initial population is 500, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P = 500 \cdot 2$$^{t/3}$$

Question 5

Which of the following is the inverse of the function $$f(x) = 3x - 7$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x+7}{3}$$

Question 6

A quadratic function models the height $$h (in $$meters) of a ball thrown upward as $$h(t) = -4.9t^2$ + 20t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

$$22.41$$ meters

Question 7

Which of the following is the correct solution to the system of equations: $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$x = 2, y = 1$$

Question 8

Which transformation occurs to the graph of $$f(x) = x^2$ when it is changed to f(x$$) = $$(x-4)^2 + 5$?

Accepted Answer

Shift right 4 units and up 5 units

Question 9

If $$f(x) = \log_{2}(x)$$, what is the value of $$f(8)$$?

Accepted Answer

$$3$$

Question 10

A car depreciates in value by 15% each year. If the initial value is $$V_0$$, which equation models the value $$V$$ after $$t$$ years?

Accepted Answer

$$V = V_0$ \cdot (0.85)^t$$

Question 11

Which of the following is the correct factorization of $$x^2 - 5x + 6$?

Accepted Answer

$$(x-2)(x-3)$$

Question 12

Given $$f(x) = x^3$ and g(x) = 2x$, what is the sum f(x) + g(x$$)$$?

Accepted Answer

$$x^3 + 2x$

Question 13

Which of the following is the correct solution to the inequality $$2x - 5 \u003c 9$$?

Accepted Answer

$$x \u003c 7$$

Question 14

If $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, what is the domain of the composition f(g(x$$))$$?

Accepted Answer

$$x \geq 0$$

Question 15

Which of the following is the correct expanded form of $$(x+2)^2$$?

Accepted Answer

$$x^2 + 4x + 4$

Question 16

A company’s revenue $$R (in $$thousands of dollars) is modeled by $$R(x) = 5x + 20$$, where $$x is $$the number of units sold. What is the revenue if 100 units are sold?

Accepted Answer

$$520$$ thousand dollars

Question 17

Which of the following is the correct solution to the equation $$e^{x} = 7$?

Accepted Answer

$$x = \ln{7}$$

Question 18

Which of the following is the correct graph for $$f(x) = -x^2$ compared to f(x$$) = $$x^2$$?

Accepted Answer

It is reflected over the x-axis

Question 19

Which of the following is the correct solution to the system of equations using matrices: $$\begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 5 \ 11 \end{bmatrix}$$?

Accepted Answer

$$x = 1, y = 2$$

College Algebra Syllabus and Study Guide

Guida di studio - Domande di pratica

Study guide - Flashcard