Free Practice Quiz Question List

01 - Functions and Mathematical Models Online Quiz Questions

Use this free practice quiz with 20 questions to review 01 - Functions and Mathematical Models, test your knowledge, and prepare for your next test or exam.

20 questions

Choose one

1 point

Which graphical condition guarantees that a relation represents a function of x?

A
Every horizontal line intersects the graph at most once.
B
The graph has no negative values.
C
Every vertical line intersects the graph at most once.
D
The graph is symmetric about the y-axis.

True or false

1 point

True or false: For any two functions f and g, the compositions $(f\circ g)(x)$ and $(g\circ f)(x)$ must be equal.

A
True
B
False

Written response

1 point

Let $f(x)=3x-4$ . What is the value of $f^{-1}(20)$ ?

Fill in the blank

1 point

Compared with the parent function $f(x)=\sqrt{x}$ , the function $g(x)=\sqrt{x+4}-1$ is shifted and .

Choose all

1 point

Select all statements that correctly describe restrictions used to determine the real-number domain of a formula.

A
The denominator of a rational expression must be nonzero.
B
The radicand of an even root must be nonnegative.
C
The argument of a logarithm may be any real number.
D
The argument of a logarithm must be positive.

True or false

1 point

True or false: In the model $P(t)=P_0b^t$ , a base satisfying $0<b<1$ represents exponential decay.

A
True
B
False

Choose one

1 point

The temperature model is $T(t)=12+3\cos\left(\frac{\pi}{6}t\right)$ , where t is measured in months. What is the model's period?

A
3 months
B
6 months
C
9 months
D
12 months

Written response

1 point

A taxi charges a fixed fee of 4 dollars plus 2.50 dollars per mile, modeled by $C(m)=4+2.50m$ . What is the cost for 6 miles?

Fill in the blank

1 point

For the height model $h(t)=-16t^2+64t+5$ , the meaningful time domain begins at and ends .

Choose all

1 point

Assuming the logarithm arguments are positive, select all valid logarithm properties.

A
$\log_b(MN)=\log_b M+\log_b N$
B
$\log_b\left(\frac{M}{N}\right)=\log_b M-\log_b N$
C
$\log_b(M+N)=\log_b M+\log_b N$
D
$\log_b(M^p)=p\log_b M$

Choose one

1 point

What does the notation $f^{-1}(x)$ mean when f is one-to-one?

A
The reciprocal of f(x)
B
The derivative of f(x)
C
The inverse function of f
D
The negative of f(x)

Open ended

1 point

In the continuous exponential model $P(t)=P_0e^{kt}$ , explain the meaning of $P_0$ and describe how the sign of k affects the model.

Choose one

1 point

At which values of x is the tangent function undefined?

A
$x=k\pi$ , where $k\in\mathbb Z$
B
$x=\frac{\pi}{2}+k\pi$ , where $k\in\mathbb Z$
C
$x=2k\pi$ , where $k\in\mathbb Z$
D
All real x

Choose one

1 point

Which test determines whether a graph represents a function of x?

A
Every horizontal line intersects the graph at most once.
B
Every vertical line intersects the graph at most once.
C
The graph must cross both coordinate axes.
D
The graph must be symmetric about the y-axis.

Choose one

1 point

What is the domain of the function g(x) = (x + 1)/(x - 3)?

A
All real numbers
B
All real numbers except -1
C
All real numbers except 3
D
Only x greater than 3

True or false

1 point

True or false: In the composition (f composed with g)(x) = f(g(x)), the function f is applied before the function g.

A
True
B
False

Choose one

1 point

What is the domain of h(x) = sqrt(x + 4) - 1?

A
[0, infinity)
B
[-4, infinity)
C
(-4, infinity)
D
(-infinity, -4]

Written response

1 point

For h(x) = sqrt(x + 4) - 1, enter the left endpoint of the domain as a number.

Choose one

1 point

Which graphical test determines whether a function has an inverse that is also a function?

A
The horizontal line test
B
The vertical line test
C
The denominator test
D
The radicand test

Written response

1 point

The temperature model T(t) = 12 + 3 cos((pi/6)t) uses t in months. Enter its period in months as a number.