Nonlinear Functions: Interactive Quizzes and Practice Questions

Question 1

What is the domain of the exponential function y = 2^(x-1)?

Accepted Answer

All real numbers

Answer

Positive real numbers only

Answer

Negative real numbers only

Answer

Integers only

Question 2

What is the y-intercept of the exponential function y = 3e^(2x)?

Accepted Answer

3

Answer

0

Answer

e^2

Answer

3e^2

Question 3

Which graph shows a quadratic function that opens upward and has a vertex at (2, -3)?

Accepted Answer

A parabola that opens upward with a vertex at (2, -3)

Answer

A parabola that opens downward with a vertex at (2, -3)

Answer

A parabola that opens upward with a vertex at (-2, -3)

Answer

A parabola that opens downward with a vertex at (-2, 3)

Question 4

Which of the following is the graph of an exponential function?

Accepted Answer

An exponential curve

Answer

A straight line

Answer

A parabola

Answer

A sinusoidal curve

Question 5

Find the equation of the line of symmetry of the graph of the function y = x^2 - 2x + 1.

Accepted Answer

x = 1

Answer

x = 0

Answer

x = 2

Answer

x = -1

Question 6

Find the inverse function of f(x) = 2x + 1.

Accepted Answer

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

Answer

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

Answer

f^-1(x) = 1/2x + 1

Answer

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

Question 7

Find the vertical asymptote of the graph of the function f(x) = 1/(x-2).

Accepted Answer

x = 2

Answer

x = 0

Answer

x = 1

Answer

x = -2

Question 8

Which of the following equations represents a parabola that opens downward?

Accepted Answer

y = -x²

Answer

y = x² + 2x + 1

Answer

y = 2x² - 3

Answer

y = 2x² + 5

Question 9

Which of the following functions is an exponential function?

Accepted Answer

y = 3^x

Answer

y = 2x + 3

Answer

y = x² - 2

Answer

y = √x

Question 10

What is the base of the exponential function y = (1/2)^x?

Accepted Answer

1/2

Answer

2

Answer

-1/2

Answer

-2

Question 11

Which of the following choices accurately describes the graph of an exponential function with a positive growth rate?

Accepted Answer

A curve that increases from left to right

Answer

A curve that decreases from left to right

Answer

A straight line with a positive slope

Answer

A straight line with a negative slope

Question 12

What is the domain of the quadratic function y = -x² + 4x + 1?

Accepted Answer

All real numbers

Answer

All positive real numbers

Answer

All negative real numbers

Answer

The empty set

Question 13

What is the range of the exponential function y = 2^x?

Accepted Answer

All positive real numbers

Answer

All real numbers

Answer

All negative real numbers

Answer

The empty set

Question 14

Which of the following graphs represents a quadratic function?

Accepted Answer

A U-shaped curve (parabola)

Answer

A straight line

Answer

A circular curve

Answer

A V-shaped curve (hyperbola)

Question 15

What is the range of the function y = (1/2)^x + 1?

Accepted Answer

{y | y > 0}

Answer

{y | y > 1}

Answer

{y | y < 0}

Answer

{y | y < 1}

Question 16

Which of the following transformations would move the graph of y = x^2 2 units up?

Accepted Answer

y = x^2 + 2

Answer

y = (x - 2)^2

Answer

y = (x + 2)^2

Answer

y = x^2 - 2

Question 17

What is the inverse of the exponential function y = 2^x?

Accepted Answer

y = log2(x)

Answer

y = x^2

Answer

y = 2(log x)

Answer

y = 1/2^x

Question 18

Find the inverse of the function f(x) = 2^x.

Accepted Answer

f^-1(x) = log2(x)

Answer

f^-1(x) = 2x

Answer

f^-1(x) = x^2

Answer

f^-1(x) = √x

Question 19

Determine the equation of a linear function with a y-intercept of 3 and a slope of -2.

Accepted Answer

y = -2x + 3

Answer

y = 2x + 3

Answer

y = -3x + 2

Answer

y = 3x + 2

Question 20

Find the value of x at which the functions f(x) = 2x + 1 and g(x) = x^2 - 1 intersect.

Accepted Answer

x = 1

Answer

x = -1

Answer

x = 0

Answer

x = 2

Question 21

Which of the following is the correct equation for a quadratic function?

Accepted Answer

y = x^2 + bx + c

Answer

y = mx + b

Answer

y = e^(bx)

Answer

y = sin(x)

Question 22

What is the constant rate of change for the exponential function y = 2^x?

Accepted Answer

2

Answer

x

Answer

2^x

Answer

x^2

Question 23

Which of the following is an example of a real-world application of a quadratic function?

Accepted Answer

Modeling the path of a projectile

Answer

Predicting the population growth of a city

Answer

Determining the area of a circle

Answer

Calculating the volume of a cone

Question 24

What is the domain of the function y = 1 / (x - 2)?

Accepted Answer

All real numbers except 2

Answer

All real numbers

Answer

Only positive real numbers

Answer

Only negative real numbers

Question 25

Select the characteristic that identifies a quadratic function that opens downwards.

Accepted Answer

Negative leading coefficient

Answer

Positive leading coefficient

Answer

Zero leading coefficient

Answer

Fractional leading coefficient

Question 26

Which transformation shifts the graph of y = 2^x one unit to the left?

Accepted Answer

y = 2^(x - 1)

Answer

y = 2^(x + 1)

Answer

y = 2^x - 1

Answer

y = 2^x + 1

Question 27

Determine the range of the function y = -2x^2 + 8x + 3.

Accepted Answer

y ≥ 3

Answer

All real numbers

Answer

y ≤ 3

Answer

y ≤ 4

Question 28

Classify the function represented by the equation y = ax^2 + bx + c (where a ≠ 0).

Accepted Answer

Quadratic function

Answer

Linear function

Answer

Exponential function

Answer

Polynomial function

Question 29

Identify the axis of symmetry for the parabola represented by the equation y = (x - 3)^2 + 2.

Accepted Answer

x = 3

Answer

x = 2

Answer

y = 2

Answer

y = 3

Question 30

Identify the characteristic that does NOT apply to exponential functions.

Accepted Answer

They have a maximum or minimum point.

Answer

They have a constant growth factor.

Answer

Their graphs are always increasing or decreasing.

Answer

They can have a y-intercept of 0.

Question 31

Find the equation of the horizontal asymptote for the exponential function y = 2^x - 1.

Accepted Answer

y = 1

Answer

y = -1

Answer

x = 1

Answer

x = -1

Question 32

Which type of graph represents a quadratic function?

Accepted Answer

Parabola

Answer

Straight line

Answer

Circle

Answer

Hyperbola

Question 33

Which transformation shifts the graph of y = x^2 leftward by 3 units?

Accepted Answer

y = (x - 3)^2

Answer

y = (x + 3)^2

Answer

y = x^2 - 3

Answer

y = x^2 + 3

Question 34

What is the equation of the axis of symmetry of a parabola with equation y = ax^2 + bx + c?

Accepted Answer

x = -b/2a

Answer

x = b/2a

Answer

y = -b/2a

Answer

y = b/2a

Question 35

Which of the following is NOT a type of exponential equation?

Accepted Answer

y = 2x + 1

Answer

y = a^x

Answer

y = x^a

Answer

y = e^x

Question 36

Which of the following graphs represents an exponential decay function?

Accepted Answer

A curve that decreases rapidly at first, then slows down

Answer

A curve that increases rapidly at first, then slows down

Answer

A straight line that slants upward

Answer

A straight line that slants downward

Question 37

Which of the following equations represents a horizontal translation of the function y = x^2 by 3 units to the right?

Accepted Answer

y = (x+3)^2

Answer

y = (x-3)^2

Answer

y = x^2 + 3

Answer

y = x^2 - 3

Question 38

Which of the following functions is a reflection of the function y = |x| over the x-axis?

Accepted Answer

y = -|x|

Answer

y = |x|

Answer

y = |x+1|

Answer

y = |x-1|

Question 39

Which of the following is the graph of a quadratic function?

Accepted Answer

A parabola that opens either upward or downward

Answer

A circle

Answer

A straight line

Answer

A hyperbola

Question 40

Which of the following is an example of an exponential function?

Accepted Answer

y = 2^x

Answer

y = 1/x

Answer

y = x^2

Question 41

What is the equation of the exponential function that passes through the points (0, 1) and (2, 4)?

Accepted Answer

y = 2^x

Answer

y = 3^x

Answer

y = 5^x

Answer

y = 4^x

Question 42

What is the domain of the function y = sqrt(x)?

Accepted Answer

x ≥ 0

Answer

x > 0

Answer

x < 0

Answer

All real numbers

Question 43

What is the equation of the line of symmetry of the graph of the function y = x^3?

Accepted Answer

x = 0

Answer

x = 1

Answer

y = 1

Answer

y = 0

Question 44

Which of the following is a characteristic of a nonlinear function?

Accepted Answer

A non-constant rate of change

Answer

A symmetrical graph

Answer

A constant rate of change

Answer

A linear graph