Question 1

Which of the following best describes a function?

Accepted Answer

A rule that assigns to each input value exactly one output value.

Question 2

Given the function $$f(x) = \sqrt{9 - x}$$, what is the domain of $$f(x)$$?

Accepted Answer

$$(-\infty, 9]$$

Question 3

Which of the following graphs passes the vertical line test and represents a function?

Accepted Answer

A graph where every vertical line crosses the curve at most once.

Question 4

If $$f(x) = 2x - 3$$, $$g(t) = 2t - 3$$, and $$C(n) = 2n - 3$$, which of the following is true?

Accepted Answer

All three represent the same function rule.

Question 5

Let $$h(x) = \ln(x-2). $$What is the domain of $$h(x)$$?

Accepted Answer

$$(2, \infty)$$

Question 6

Suppose $$f(x) = 3x + 1. $$What is $$f(x+h)$$?

Accepted Answer

$$3x + 3h + 1$$

Question 7

Given $$f(x) = x^2$ + 3$$ and $$g(x) = 4x - 1$$, what is $$(f+g)(x)$$?

Accepted Answer

$$x^2 + 4x + 2$

Question 8

If $$f(x) = x^2$ + 3$$, $$g(x) = 4x - 1$$, and $$h(x) = e^x$$, what is $$y = \frac{f(x)}{g(x)} - 3h(x)$$?

Accepted Answer

$$\frac{x^2$ + 3}{4x - 1} - 3e^x$$

Question 9

What is the difference quotient for $$f(x) = x - 2x^2$?

Accepted Answer

$$1 - 4x - 2h$$

Question 10

Let $$f(x) = x - 5$$ and $$g(x) = 0.75x. If $$you use the coupon first and then the store discount, what is the resulting function $$h(x)$$?

Accepted Answer

$$h(x) = 0.75(x - 5)$$

Question 11

Given the piecewise function $$f(x) = \begin{cases} x+6 & -3 \leq x \u003c 0 \ -x^2$+5 & 0 \leq x \u003c 2 \ 3 & 2 \leq x \leq 5 \end{cases}$$, what is $$f(1)$$?

Accepted Answer

$$4$$

Question 12

For the function $$f(x) = \frac{1}{(x+3)(x-1)}$$, what is the domain?

Accepted Answer

$$(-\infty, -3) \cup (-3, 1) \cup (1, \infty)$$

Question 13

If $$f(x) = 2x - 1$$ and $$g(x) = e^x$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$2e^x - 1$$

Question 14

Which of the following is NOT a function?

Accepted Answer

A relation where an input value is assigned to two different output values.

Question 15

Given $$f(x) = x^2$ + 3$$ and $$g(x) = 4x - 1$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$(4x - 1)^2$ + 3$$

Question 16

If $$y = e$$^{2x}$$, decompose this as a composition of two functions f$ and g$ such that y = f(g(x$$))$$.

Accepted Answer

$$f(u) = e^u$$, $$g(x) = 2x$$

Question 17

A medical test result is modeled by $$T(x) = \sqrt{1 + x^2$}$$, where $$x is a $$measured value. What is the domain of $$T(x)$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 18

A chemical reaction rate is given by $$R(t) = \ln(t-2)$$, where $$t is $$time in seconds. For which values of $$t is $$the reaction rate defined?

Accepted Answer

$$t \u003e 2$$

Study Guide: Basics of Functions for Calculus

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