Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{x+4}$$?

Accepted Answer

$$[-4, \infty)$$

Question 2

Given $$f(x) = x^2$ + 4$$, what is the range of $$f(x)$$?

Accepted Answer

$$[4, \infty)$$

Question 3

Suppose $$f(x) = x^3$ and g(x$$) = $$x^2 - 3$. What is (f$$ \circ g)(x)$$?

Accepted Answer

$$(x^2$$ - $$3)^3$$

Question 4

Which of the following statements is true about even and odd functions?

Accepted Answer

The sum of two even functions is always even.

Question 5

For the function $$f(x) = x^n$$ where $$n is a $$positive integer, which of the following is true?

Accepted Answer

If $$n is $$even, $$f(x) is $$even.

Question 6

The difference quotient for a function $$f(x) is $$given by:

Accepted Answer

$$\dfrac{f(x+h) - f(x)}{h}$$

Question 7

Which graph represents a function that is symmetric about the origin?

Accepted Answer

$$f(x) = x^3$

Question 8

If $$f(x) = x^2$ and g(x$$) = $$x^3$$, what is $$f(x) + g(x)$$? Is the resulting function even, odd, or neither?

Accepted Answer

Neither

Question 9

Which of the following is the correct inverse of $$f(x) = x^2$ + 3$$ for $$x \geq 0$$?

Accepted Answer

$$f^{-1}(x$$) = \sqrt{x - 3}$$

Question 10

The graph of the inverse function $$f^{-1}(x$$)$$ is the reflection of the graph of f(x$$)$$ about which line?

Accepted Answer

$$y = x$$

Question 11

Which of the following is a property of logarithms?

Accepted Answer

$$\log_b(xy) = \log_b(x) + \log_b(y)$$

Question 12

If $$f(x) = \sqrt{x}$$, what is the range of $$f(x)$$?

Accepted Answer

$$[0, \infty)$$

Question 13

Which of the following functions is neither even nor odd?

Accepted Answer

$$f(x) = x + 1$$

Question 14

Given $$f(x) = x^2$ and g(x$$) = $$x^3$$, which of the following is $$(g \circ f)(x)$$?

Accepted Answer

$$(x^2)^3$

Question 15

Which of the following is the correct domain for $$f(x) = \frac{1}{x}$$?

Accepted Answer

$$(-\infty, 0) \cup (0, \infty)$$

Question 16

If $$f(x) = x^2$ and g(x$$) = $$x^3$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$(x^3)^2$

Question 17

Which of the following is the correct property of logarithms for division?

Accepted Answer

$$\log_b\left(\frac{x}{y}\right) = \log_b(x) - \log_b(y)$$

Question 18

Which of the following is the correct slope formula for the secant line between $$x$$ and $$x+h$$ for a function $$f(x)$$?

Accepted Answer

$$\dfrac{f(x+h) - f(x)}{h}$$

Question 19

If $$f(x) = x^2$ and g(x$$) = $$x^3$$, which of the following is $$f(x) - g(x)$$?

Accepted Answer

$$x^2$$ - $$x^3$$

Functions, Their Properties, and Inverses: Calculus Foundations

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