$x \neq \frac{\pi}{2} + k\pi$, $k \in \mathbb{Z}$

Question 1

Which of the following is the correct quadratic formula for finding the roots of $ax^2 + bx + c = 0$?

Accepted Answer

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Question 2

Given the function $f(x) = x^2$, what is the domain and range of $f(x)$?

Accepted Answer

Domain: $(-\infty, \infty)$, Range: $[0, \infty)$

Question 3

If $\log_a b = x$, which of the following is equivalent to this statement?

Accepted Answer

$a^x = b$

Question 4

Which property of logarithms allows you to write $\log_a (xy) = \log_a x + \log_a y$?

Accepted Answer

Product property

Question 5

Solve for $x$: $2^x = 16$

Accepted Answer

$x = 4$

Question 6

Which of the following is the correct definition of the range of a function $f$?

Accepted Answer

The set of all outputs of the function

Question 7

Given $f(x) = x^2$ and $f(x+h) = (x+h)^2$, what is $f(x+h) - f(x)$?

Accepted Answer

$2xh + h^2$

Question 8

Which of the following is the equation of a line in slope-intercept form?

Accepted Answer

$y = mx + b$

Question 9

A line passes through the points $(2,3)$ and $(4,9)$. What is its equation in slope-intercept form?

Accepted Answer

$y = 3x - 3$

Question 10

Convert $90^\circ$ to radians.

Accepted Answer

$\frac{\pi}{2}$

Question 11

Which trigonometric function has a range of $[-1, 1]$?

Accepted Answer

$y = \sin x$

Question 12

What is $	an \frac{\pi}{2}$?

Accepted Answer

Does not exist (DNE)

Question 13

If $\log_2 x = 5$, what is $x$?

Accepted Answer

$32$

Question 14

Which of the following is the correct property for exponents: $(a^x)^y$?

Accepted Answer

$a^{xy}$

Question 15

Given $y = 	an x$, what is the domain of $y$?

Accepted Answer

$x 
eq \frac{\pi}{2} + k\pi$, $k \in \mathbb{Z}$

Question 16

Which of the following is the correct inverse relationship between logarithms and exponents?

Accepted Answer

$\log_a (a^x) = x$

Question 17

If $f(x) = x^2$ and $f(3) = 9$, what is $f(x+2)$?

Accepted Answer

$x^2 + 4x + 4$

Question 18

Which of the following is the correct formula for the slope of a line passing through $(x_1, y_1)$ and $(x_2, y_2)$?

Accepted Answer

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Question 19

Which of the following is the correct conversion from radians to degrees?

Accepted Answer

Multiply by $\frac{180}{\pi}$

Foundations of Calculus: Algebra, Functions, and Trigonometry

Study Guide - Practice Questions