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

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

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