Question 1

Which of the following best describes the domain of the function $$f(x) = \dfrac{1}{x-3}$$?

Accepted Answer

All real numbers except $$x = 3$$

Question 2

Given the function $$f(x) = x^2$ - 4x + 3$$, what are the $$x-$$intercepts?

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 3

Which of the following is the inverse of the function $$f(x) = 2x + 5$$?

Accepted Answer

$$f^{-1}(x$$) = \dfrac{x-5}{2}$$

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

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

Question 5

Which of the following functions is NOT one-to-one?

Accepted Answer

$$f(x) = x^2$

Question 6

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

Accepted Answer

$$(f \circ g)(2) = 9$$

Question 7

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

$$h_{max} = 22.4$$ meters

Question 8

Which of the following is the correct equation for the line passing through $$(2, 5)$$ with slope $$-3$$?

Accepted Answer

$$y - 5 = -3(x - 2)$$

Question 9

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

Accepted Answer

$$(x, y) = (2, 3)$$

Question 10

Which of the following best describes the range of the function $$f(x) = \sqrt{x-2}$$?

Accepted Answer

$$[0, \infty)$$

Question 11

A car's value depreciates exponentially according to $$V(t) = 20000 \cdot (0.85)^t$$, where $$t is $$the number of years after purchase. What is the value after 3 years?

Accepted Answer

$$V(3) \approx 12206$$

Question 12

Which of the following is the correct transformation for $$f(x) = x^2$ to g(x$$) = $$(x-4)^2 + 2$?

Accepted Answer

Shift right 4 units and up 2 units

Question 13

Which of the following is the correct solution to $$|2x - 5| = 7$$?

Accepted Answer

$$x = 6 or$$ $$x = -1$$

Question 14

Which of the following is the correct equation for a circle with center $$(3, -2)$$ and radius $$5$$?

Accepted Answer

$$(x - 3)^2$ + (y + 2)^2$ = 25$$

Question 15

Given $$f(x) = \dfrac{2x+1}{x-1}$$, what is the horizontal asymptote?

Accepted Answer

$$y = 2$$

Question 16

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

Accepted Answer

$$x = 32$$

Question 17

A company’s revenue $$R (in $$thousands of dollars) is modeled by $$R(x) = 4x^2$ + 20x + 100$$, where $$x is $$the number of years since opening. What is the revenue after 3 years?

Accepted Answer

$$R(3) = 202$$

Question 18

Which of the following is the correct solution to the system of equations using matrices: $$\begin{cases} x + 2y = 8 \ 3x - y = 7 \end{cases}$$?

Accepted Answer

$$(x, y) = (3, 2.5)$$

Question 19

Which of the following best describes the graph of $$y = -x^2$ + 4x - 1$$?

Accepted Answer

A downward-opening parabola with vertex at $$(2, 3)$$

MAT 151 College Algebra/Functions – Syllabus and Study Guide

Guida di studio - Domande di pratica

Study guide - Flashcard