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

$$f(g(2)) = 2 \times 4 + 1 = 9$$

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

$$a \u003e 0$$ 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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