Q: Given $f(x) = \frac{2x}{x^2 - 2}$ and $g(x) = \frac{2x + 3}{x}$, are $f$ and $g$ inverses of each other?

No, because $f(g(x)) \neq x$ for all $x$ in the domain.

Question 1

Which of the following sets represents the graph of a function?

Accepted Answer

$\{(-1, -4), (2, -1), (6, -5), (8, 3), (10, 3)\}$

Question 2

Given $f(x) = x^2 - 2x - 7$, what is $f(3)$?

Accepted Answer

$-4$

Question 3

How can the graph of $f(x) = -\sqrt{x-4}$ be obtained from the graph of $y = \sqrt{x}$?

Accepted Answer

Shift 4 units to the right and reflect across the $x$-axis.

Question 4

Which of the following graphs is NOT the graph of a function?

Accepted Answer

A graph that fails the vertical line test.

Question 5

Given $f(x) = \frac{2x}{x^2 - 2}$ and $g(x) = \frac{2x + 3}{x}$, are $f$ and $g$ inverses of each other?

Accepted Answer

No, because $f(g(x)) 
eq x$ for all $x$ in the domain.

Question 6

If $f(x) = x + 5$ and $g(x) = x - 4$, what is $(f - g)(x)$?

Accepted Answer

$9$

Question 7

Given $f(x) = 5x^2 - 5$ and $g(x) = 3x^2 - 5x - 4$, what is $(f + g)(x)$?

Accepted Answer

$8x^2 - 5x - 9$

Question 8

Determine algebraically whether the function $f(x) = x^2 + x^3$ is even, odd, or neither.

Accepted Answer

Neither

Question 9

Which of the following describes the symmetry of $y = x^2 - 4$?

Accepted Answer

Symmetric with respect to the $y$-axis only.

Question 10

Find the distance between the points $(7, 7)$ and $(-6, -7)$.

Accepted Answer

$\sqrt{365}$

Question 11

What is the equation of the circle with center $(-8, 6)$ and radius $3$?

Accepted Answer

$(x + 8)^2 + (y - 6)^2 = 9$

Question 12

A real-world scenario: A company’s profit $P$ in thousands of dollars is modeled by $P(x) = -2x^2 + 8x + 10$, 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 $18$ thousand dollars at $x = 2$ thousand units.

Question 13

Given the line passing through $(3, 5)$ with slope $m = -3$, what is its equation in point-slope form?

Accepted Answer

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

Question 14

Which of the following statements about the function $f(x) = x^4 + 2x + 8$ is true?

Accepted Answer

It is neither even nor odd.

Question 15

A hospital monitors the temperature of a patient every hour. The temperature $T$ in degrees Celsius is modeled by $T(t) = -0.5t^2 + 2t + 37$, where $t$ is the number of hours after admission. What is the maximum temperature and at what time does it occur?

Accepted Answer

Maximum temperature is $39$°C at $t = 2$ hours.

Question 16

Which of the following is the slope-intercept form of the equation passing through $(9, 5)$ and $(0, -3)$?

Accepted Answer

$y = \frac{8}{9}x - 3$

Question 17

Given $f(x) = 16 - x^2$ and $g(x) = 4 - x$, what is $(f \div g)(x)$?

Accepted Answer

$\frac{16 - x^2}{4 - x}$

Question 18

A circle has the equation $(x - 8)^2 + (y - 8)^2 = 64$. What is the center and radius of the circle?

Accepted Answer

Center $(8, 8)$, radius $8$

Question 19

Which of the following best describes the transformation to obtain the graph of $f(x) = x^2 - 2x - 7$ from $y = x^2$?

Accepted Answer

Shift 1 unit right and 7 units down.

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