Question 1

Which of the following best describes the graph of the constant function $$f(x) = c$$?

Accepted Answer

A horizontal line crossing the y-axis at $$y = c$$

Question 2

What is the domain and range of the identity function $$f(x) = x$$?

Accepted Answer

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

Question 3

The graph of $$f(x) = x^2$ is a parabola. Which of the following statements is true about its domain and range?

Accepted Answer

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

Question 4

Which function has a graph that passes through the origin and is symmetric with respect to the origin?

Accepted Answer

$$f(x) = x^3$

Question 5

A medical researcher models the growth of bacteria using the function $$f(x) = x^2$. If x$ represents time in hours, what is the minimum number of bacteria present at any time?

Accepted Answer

0

Question 6

Which of the following functions is NOT defined for negative values of $$x$$?

Accepted Answer

$$f(x) = \sqrt{x}$$

Question 7

A cube root function $$f(x) = \sqrt[3]{x} is $$used to model the dosage of a medication based on patient weight $$x. $$What is the domain of this function?

Accepted Answer

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

Question 8

Which function's graph increases more rapidly as $$x$$ increases: $$f(x) = x^2$ or f(x$$) = $$x^3$$?

Accepted Answer

$$f(x) = x^3$

Question 9

If the output of a function is always the same regardless of the input, which type of function is this?

Accepted Answer

Constant function

Question 10

A square root function $$f(x) = \sqrt{x} is $$used to estimate the time required for a chemical reaction to complete, where $$x is $$the concentration of a reactant. What is the range of this function?

Accepted Answer

$$[0, \infty)$$

Question 11

Which function is used to model situations where the output is the square of the input, such as calculating the area of a square given its side length?

Accepted Answer

$$f(x) = x^2$

Question 12

Which of the following functions is an example of an odd function?

Accepted Answer

$$f(x) = x^3$

Question 13

A cube function $$f(x) = x^3$ is used to model the volume of a cube with side length x$. If x$ is doubled, by what factor does the volume increase?

Accepted Answer

8

Question 14

Which function's graph is a straight line passing through the origin with a slope of 1?

Accepted Answer

$$f(x) = x$$

Question 15

If $$f(x) = \sqrt{x}$$, what is $$f(16)$$?

Accepted Answer

4

Question 16

Which function is used to model the relationship between the side length and the area of a square?

Accepted Answer

$$f(x) = x^2$

Question 17

Which function is defined for all real numbers and has a range of all real numbers?

Accepted Answer

$$f(x) = x^3$

Question 18

A square root function $$f(x) = \sqrt{x} is $$used to model the speed of a car as a function of the engine power $$x. If $$the engine power is quadrupled, by what factor does the speed increase?

Accepted Answer

2

Question 19

Which function's graph is symmetric about the y-axis?

Accepted Answer

$$f(x) = x^2$

Question 20

If $$f(x) = x^2$ and g(x$$) = $$x^3$$, which function grows faster for large positive values of $$x$$?

Accepted Answer

$$g(x) = x^3$

Graphs of Common Functions in College Algebra

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