Question 1

Which of the following is the correct formula for the distance between two points $A(x_1, y_1)$ and $B(x_2, y_2)$ in the coordinate plane?

Accepted Answer

$\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Question 2

A biologist is tracking the population of a species using the function $P(t) = 500e^{0.03t}$, where $t$ is the number of years since the study began. What is the population after 10 years?

Accepted Answer

$500e^{0.3} \approx 674$

Question 3

Which of the following describes the graph of the function $f(x) = |x|$?

Accepted Answer

A V-shaped graph opening upwards with vertex at $(0,0)$

Question 4

Given the equation $2x - 3y = 6$, what is the slope of the line?

Accepted Answer

$-\frac{2}{3}$

Question 5

A company’s profit $P$ in thousands of dollars is modeled by $P(x) = -2x^2 + 8x + 5$, where $x$ is the number of units sold (in thousands). What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $13$ thousand dollars at $x = 2$ thousand units

Question 6

Which transformation results in the graph of $f(x) = x^2$ being shifted 3 units to the left?

Accepted Answer

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

Question 7

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

Accepted Answer

$f(g(2)) = 2 	imes 4 + 1 = 9$

Question 8

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

Accepted Answer

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

Question 9

A linear function $f(x)$ passes through the points $(1, 4)$ and $(3, 10)$. What is the equation of the function in slope-intercept form?

Accepted Answer

$f(x) = 2x + 2$

Question 10

Which of the following is NOT a function?

Accepted Answer

The equation $x = y^2$

Question 11

A medication’s concentration in the bloodstream is modeled by $C(t) = 20e^{-0.5t}$, where $t$ is hours after administration. What is the concentration after 4 hours?

Accepted Answer

$20e^{-2} \approx 2.71$

Question 12

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

Accepted Answer

All real numbers except $x = 3$

Question 13

A line passes through $(2, 5)$ and is perpendicular to the line $y = -\frac{1}{2}x + 3$. What is the equation of the perpendicular line in point-slope form?

Accepted Answer

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

Question 14

Which of the following transformations will reflect the graph of $f(x)$ over the $y$-axis?

Accepted Answer

$f(-x)$

Question 15

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

Accepted Answer

$f(3) + g(3) = 9 + 4 = 13$

Question 16

Which of the following is the correct formula for the midpoint of the segment joining $(x_1, y_1)$ and $(x_2, y_2)$?

Accepted Answer

$\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$

Question 17

A quadratic function $f(x) = ax^2 + bx + c$ opens upwards and has its vertex at $(2, -5)$. Which of the following must be true?

Accepted Answer

$a > 0$ and the minimum value is $-5$ at $x = 2$

Question 18

Which of the following is the correct way to write the equation $x^2 + 6x + 5 = 0$ in factored form?

Accepted Answer

$(x + 1)(x + 5) = 0$

Question 19

A function $f(x)$ is decreasing on the interval $(-\infty, 0)$ and increasing on $(0, \infty)$. Which of the following could be the graph of $f(x)$?

Accepted Answer

A parabola opening upwards with vertex at $(0, y)$

College Algebra: Core Concepts and Functions Study Guide

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