Q: Which of the following matrices is invertible?

$$\begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$$

Q: Which of the following best describes the end behavior of the polynomial $$f(x) = -2x^5$ + 3x^2$ - 7$$?

As $$x \to \infty$$, $$f(x) \to -\infty$$; as $$x \to -\infty$$, $$f(x) \to \infty$$

Question 1

Which of the following is the correct definition of a function?

Accepted Answer

A relation in which each input is paired with exactly one output.

Question 2

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

Accepted Answer

$$f(-2) = 17$$

Question 3

Which of the following graphs represents a function that is one-to-one?

Accepted Answer

A straight line with a nonzero slope.

Question 4

If $$g(x) = \sqrt{x-1}$$, what is the domain of $$g(x)$$?

Accepted Answer

$$x \geq 1$$

Question 5

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

Accepted Answer

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

Question 6

A population of bacteria triples every 4 hours. If the initial population is 200, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P = 200 	imes 3$$^{t/4}$$

Question 7

Solve for $$x$$: $$2^{x+1} = 32$

Accepted Answer

$$x = 4$$

Question 8

Which of the following is a solution to the equation $$\log_2$(x) = 5$$?

Accepted Answer

$$x = 32$$

Question 9

Given the system of equations: $$\begin{cases} 2x + 3y = 7 \ 4x - y = 5 \end{cases}$$, what is the value of $$x$$?

Accepted Answer

$$x = 2$$

Question 10

Which of the following matrices is invertible?

Accepted Answer

$$\begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix}$$

Question 11

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

Accepted Answer

$$20.41$$ meters

Question 12

Which of the following is the correct factorization of $$x^2 - 9x + 20$?

Accepted Answer

$$(x-4)(x-5)$$

Question 13

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

Accepted Answer

$$9$$

Question 14

Which of the following best describes the end behavior of the polynomial $$f(x) = -2x^5$ + 3x^2$ - 7$$?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o -\infty$$; as $$x 	o -\infty$$, $$f(x) 	o \infty$$

Question 15

A chemical reaction is modeled by the exponential decay function $$C(t) = 100e$$^{-0.05t}$$, where C$ is the concentration in mg/L and t$ is time in minutes. What is the concentration after 20 minutes?

Accepted Answer

$$C(20) \approx 60.65 mg/L$$

Question 16

Which of the following is the solution set for the inequality $$x^2 - 4x$$ \u003c 5$$?

Accepted Answer

$$2 - \sqrt{9} \u003c x \u003c 2 + \sqrt{9}$$

Question 17

Which of the following statements about the determinant of a matrix is true?

Accepted Answer

A matrix is invertible if and only if its determinant is not zero.

Question 18

A medical test result is modeled by the function $$T(x) = \frac{1}{1+e$$^{-x}$$}. If$$ $$x = 0$$, what is the value of $$T(x)$$?

Accepted Answer

$$0.5$$

Question 19

Which of the following is the correct solution to the equation $$|2x - 5| = 9$$?

Accepted Answer

$$x = 7 or$$ $$x = -2$$

Question 20

A company’s profit $$P (in $$thousands of dollars) is modeled by $$P(x) = -2x^2$ + 12x - 16$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit?

Accepted Answer

$$P = 20$$ thousand dollars

College Algebra Syllabus and Course Outline Study Guide

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드