Question 1

Which of the following functions has a domain of all real numbers except $$x = 0$$?

Accepted Answer

$$f(x) = \dfrac{1}{x}$$

Question 2

The graph of $$f(x) = x^2$ is reflected over the x$-axis and translated down 1 unit. What is the equation of the new function?

Accepted Answer

$$f(x) = -x^2$ - 1$$

Question 3

Which function is even?

Accepted Answer

$$f(x) = x^2$

Question 4

Which of the following best describes the range of the square root function $$f(x) = \sqrt{x}$$?

Accepted Answer

$$[0, \infty)$$

Question 5

A satellite dish is designed using the reflection property of which basic function?

Accepted Answer

$$f(x) = x^2$

Question 6

Which function has a 'corner' at the origin, where the graph changes direction abruptly?

Accepted Answer

$$f(x) = |x|$$

Question 7

The function $$f(x) = \lfloor x \rfloor is $$best described as:

Accepted Answer

A function with a jump discontinuity at every integer

Question 8

Which function models population growth with an upper limit, such as in biology or business?

Accepted Answer

$$f(x) = \dfrac{1}{1 + e$$^{-x}$$}$$

Question 9

Which of the following statements is true about the function $$f(x) = \sin x$$?

Accepted Answer

It is an odd function

Question 10

The function $$f(x) = \ln x$$ increases very slowly. What is its domain?

Accepted Answer

$$(0, \infty)$$

Question 11

Which function has a point of inflection at the origin?

Accepted Answer

$$f(x) = x^3$

Question 12

Which of the following functions is neither even nor odd?

Accepted Answer

$$f(x) = \ln x$$

Question 13

Suppose a function $$f(x) is $$symmetric with respect to the $$y-$$axis. Which property does it have?

Accepted Answer

It is an even function

Question 14

Which function has local extrema at the zeros of the sine function?

Accepted Answer

$$f(x) = \cos x$$

Question 15

A real-world application of the exponential function $$f(x) = e^x is$$:

Accepted Answer

Modeling continuous compound interest

Question 16

Which function is defined for all real numbers and leaves every real number unchanged?

Accepted Answer

$$f(x) = x$$

Question 17

Which function has a vertical asymptote at $$x = 0$$ and is used in satellite dish design?

Accepted Answer

$$f(x) = \dfrac{1}{x}$$

Question 18

If $$f(x) = -x^2$ - 1$$, on what interval is the function increasing?

Accepted Answer

$$(-\infty, 0)$$

Question 19

Which function has two horizontal asymptotes, $$y = 0$$ and $$y = 1$$?

Accepted Answer

$$f(x) = \dfrac{1}{1 + e$$^{-x}$$}$$

Question 20

Which of the following is true about the function $$f(x) = |x|$$?

Accepted Answer

It is even

The Twelve Basic Functions in Precalculus: Properties and Graphical Analysis

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