Functions: Master the Basics of Functions in Math

Question 1

Which graph represents a linear function? Select the correct option.

Accepted Answer

A straight line

Answer

A parabola

Answer

A hyperbola

Answer

An ellipse

Question 2

Identify the domain of the exponential function f(x) = 2^x. Select the correct option.

Accepted Answer

All real numbers

Answer

Only positive real numbers

Answer

Only non-negative real numbers

Answer

Only numbers greater than 1

Question 3

Determine the asymptote of the logarithmic function f(x) = log2(x + 1). Select the correct value.

Accepted Answer

x = -1

Answer

x = 0

Answer

x = 1

Answer

x = 2

Question 4

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 5

Which of the following represents a composition of functions? Select the correct option.

Accepted Answer

f(g(x))

Answer

g(f(x))

Answer

f(x) + g(x)

Answer

f(x) - g(x)

Question 6

Identify the range of the function f(x) = -x^2 + 4. Select the correct option.

Accepted Answer

All real numbers greater than or equal to -4

Answer

All real numbers less than or equal to 4

Answer

All real numbers between -4 and 4

Answer

All real numbers

Question 7

Which of the following functions is increasing? Select the correct function.

Accepted Answer

f(x) = x^3

Answer

f(x) = -x^2

Answer

f(x) = 1/x

Answer

f(x) = log2(x)

Question 8

Which equation represents a quadratic function?

Accepted Answer

y = x^2 - 3x + 2

Answer

y = 2x + 5

Answer

y = e^x

Answer

y = sin(x)

Question 9

What is the domain of the function f(x) = log(x + 2)?

Accepted Answer

x > -2

Answer

All real numbers

Answer

x ≤ -2

Answer

x ≠ -2

Question 10

The range of the function f(x) = |x - 1| is:

Accepted Answer

All real numbers

Answer

x ≥ 0

Answer

x ≤ 0

Answer

x ≥ 1

Question 11

The function f(x) = 2^x is:

Accepted Answer

Exponential

Answer

Linear

Answer

Quadratic

Answer

Logarithmic

Question 12

What is the period of the graph of the function f(x) = sin(x)?

Accepted Answer

2π

Answer

π

Answer

1

Answer

π/2

Question 13

Which function is increasing on the interval (-∞, ∞)?

Accepted Answer

f(x) = e^x

Answer

f(x) = x^3

Answer

f(x) = -x^2

Answer

f(x) = sin(x)

Question 14

What is the equation of a line that has a slope of 2 and a y-intercept of -3?

Accepted Answer

y = 2x - 3

Answer

y = -2x - 3

Answer

y = 2x + 3

Answer

y = -2x + 3

Question 15

Which of the following is an exponential function?

Accepted Answer

y = 2^x

Answer

y = x^2

Answer

y = log(x)

Answer

y = sin(x)

Question 16

What is the domain of the logarithmic function y = log(x + 1)?

Accepted Answer

x > -1

Answer

x > 0

Answer

x < 0

Answer

x < -1

Question 17

Which graph represents an increasing function?

Accepted Answer

A graph that slopes upward from left to right

Answer

A graph that slopes downward from left to right

Answer

A graph that is a horizontal line

Answer

A graph that is a vertical line

Question 18

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

Accepted Answer

The growth of a bacterial population

Answer

The trajectory of a thrown ball

Answer

The boiling of water

Answer

The speed of a car

Question 19

Which transformation would move the graph of the function f(x) = x^2 left by 2 units?

Accepted Answer

f(x - 2)

Answer

f(x + 2)

Answer

f(2x)

Answer

f(x)/2

Question 20

What is the equation of the line that passes through the points (2, 5) and (4, 9)?

Accepted Answer

y = 2x + 1

Answer

y = 2x - 1

Answer

y = x + 3

Answer

y = x - 3

Question 21

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

Accepted Answer

A straight line intersecting the origin

Answer

A parabola opening upward or downward

Answer

An exponential curve approaching infinity

Answer

A logarithmic curve approaching zero

Question 22

Which of the following functions has a graph that is symmetrical about the y-axis?

Accepted Answer

y = |x|

Answer

y = x^2

Answer

y = e^x

Answer

y = ln(x)

Question 23

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

Accepted Answer

2

Answer

x

Answer

y

Answer

e

Question 24

What is the domain of the logarithmic function y = log(x - 1)?

Accepted Answer

x > 1

Answer

x < 1

Answer

x > 0

Answer

x < 0

Question 25

Which of the following transformations would shift the graph of the function y = x^2 to the left 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 26

What is the equation of the line that passes through the point (2, 5) and has a slope of -3?

Accepted Answer

y = -3x + 11

Answer

y = 3x - 1

Answer

y = -3x - 1

Answer

y = 3x + 11

Question 27

Which of the following graphs represents a quadratic function?

Accepted Answer

A parabola

Answer

A line

Answer

A circle

Answer

A hyperbola

Question 28

Which of the following functions has a vertical asymptote at x = 2?

Accepted Answer

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

Answer

f(x) = e^x

Answer

f(x) = ln(x)

Answer

f(x) = x^2

Question 29

Which property describes a function whose graph is symmetric with respect to the y-axis?

Accepted Answer

Even function

Answer

Odd function

Answer

Linear function

Answer

Quadratic function

Question 30

To shift the graph of y = f(x) down by 2 units, which transformation should be applied?

Accepted Answer

y = f(x) - 2

Answer

y = f(x) = 2

Answer

y = f(x - 2)

Answer

y = f(x + 2)

Question 31

Determine the equation that represents a linear function:

Accepted Answer

y = 2x + 3

Answer

y = 3^x

Answer

y = x^2 - 2x + 1

Answer

y = e^(x-2)

Question 32

Identify the composite function from the following:

Accepted Answer

y = e^(log(x))

Answer

y = sin(x)

Answer

y = x^2 + 2x

Answer

y = 3^x

Question 33

Which equation represents a linear function with a slope of 2 and a y-intercept of 3?

Accepted Answer

y = 2x + 3

Answer

y = x + 6

Answer

y = 3x + 2

Answer

y = 2x - 3

Question 34

What is the asymptote of the logarithmic function y = log(x - 1)?

Accepted Answer

x = 1

Answer

x = 0

Answer

y = 0

Answer

y = 1

Question 35

What is the domain of the function y = |x - 2|?

Accepted Answer

All real numbers

Answer

x ≤ 2

Answer

x ≥ 2

Answer

x ≠ 2

Question 36

Which of the following is the equation of the vertical asymptote of the rational function y = (x + 1) / (x - 2)?

Accepted Answer

x = 2

Answer

x = 1

Answer

y = 1

Answer

y = 2

Question 37

What is the amplitude of the trigonometric function y = 2cos(3x)?

Accepted Answer

2

Answer

1

Answer

3

Answer

6

Question 38

What are the coordinates of the vertex of the parabola represented by the equation y = x^2 - 4x + 3?

Accepted Answer

(2, -1)

Answer

(1, -2)

Answer

(2, 1)

Answer

(1, 2)

Question 39

Which of the following graphs represents an exponential function with a base greater than 1?

Accepted Answer

A curve that increases rapidly as x increases

Answer

A curve that decreases rapidly as x increases

Answer

A line that increases steadily as x increases

Answer

A line that decreases steadily as x increases

Question 40

What is the domain of the logarithmic function log(x - 2)?

Accepted Answer

x > 2

Answer

x < 2

Answer

x > 0

Answer

All real numbers

Question 41

Which of the following functions is a translation of the function f(x) = |x| 2 units to the left?

Accepted Answer

f(x) = |x - 2|

Answer

f(x) = |x + 2|

Answer

f(x) = |x| + 2

Answer

f(x) = |x| - 2

Question 42

What is the inverse of the function f(x) = 3x + 2?

Accepted Answer

f^-1(x) = (x - 2)/3

Answer

f^-1(x) = (x - 2) / -3

Answer

f^-1(x) = (x + 2) / 3

Answer

f^-1(x) = (x + 2) / -3

Question 43

What is the range of the function f(x) = 2^x?

Accepted Answer

All positive real numbers

Answer

All real numbers

Answer

All rational numbers

Answer

All integers

Question 44

Which of the following functions is a linear function?

Accepted Answer

f(x) = 3x - 1

Answer

f(x) = x^2 + 2x

Answer

f(x) = 2^x

Answer

f(x) = log(x)

Question 45

Which of the following is the equation of the exponential function that passes through the points (0, 2) and (2, 8)?

Accepted Answer

f(x) = 4^(x)

Answer

f(x) = 2^(x)

Answer

f(x) = 8^(x)

Answer

f(x) = 16^(x)

Question 46

What is the domain of the logarithmic function f(x) = log(x + 2)?

Accepted Answer

x > -2

Answer

All real numbers

Answer

x > 0

Answer

No solution

Question 47

Find the vertex of the parabola represented by the equation f(x) = -x^2 + 4x + 5.

Accepted Answer

(2, 9)

Answer

(4, 5)

Answer

(2, 1)

Answer

(-2, 1)

Question 48

What is the range of the function f(x) = |x|?

Accepted Answer

Only non-negative real numbers

Answer

All real numbers

Answer

Only positive real numbers

Answer

No solution

Question 49

Which of the following is a transformation of the function f(x) = x^2?

Accepted Answer

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

Answer

f(x) = -x^2

Answer

f(x) = x^2 + 3

Answer

f(x) = 2x^2

Question 50

Which of the following is the equation of a parabola with vertex at (2, 3)?

Accepted Answer

y = (x - 2)² + 3

Answer

y = (x + 2)² + 3

Answer

y = (x - 3)² + 2

Answer

y = (x + 3)² + 2

Question 51

Which of the following is the inverse of the logarithmic function f(x) = log₂(x)?

Accepted Answer

y = 2^x

Answer

y = log₂(x)

Answer

y = 2^(1/x)

Answer

y = x²

Question 52

Which of the following is the asymptote of the exponential function f(x) = e^(-x)?

Accepted Answer

y = 0

Answer

x = 0

Answer

x = 1

Answer

y = 1

Question 53

What is the range of the function f(x) = |x - 2|?

Accepted Answer

All non-negative real numbers

Answer

All real numbers less than or equal to 2

Answer

All real numbers greater than or equal to 2

Answer

All real numbers

Question 54

Which is not a characteristic of a quadratic function?

Accepted Answer

Asymptote

Answer

U-shaped graph

Answer

Single turning point

Answer

Can have negative values

Question 55

What is the vertex of the parabola y equals x squared minus 4x plus 3?

Accepted Answer

(2, -1)

Answer

(0, 3)

Answer

(3, -4)

Answer

(-2, 7)

Question 56

What is the range of the function f(x) equals 2 to the power of x?

Accepted Answer

y is greater than 0

Answer

y is less than 2

Answer

y is less than 0

Answer

y is greater than 2

Question 57

Which transformation shifts a graph right by 2 units?

Accepted Answer

f(x minus 2)

Answer

f(x) plus 2

Answer

f(x) equals 2

Answer

f(x) equals 2x

Question 58

What is the inverse operation of finding the logarithm of a number?

Accepted Answer

Exponentiation

Answer

Multiplication

Answer

Division

Answer

Subtraction

Question 59

Which of the following graphs represents a linear function?

Accepted Answer

A straight line

Answer

A parabola

Answer

A circle

Answer

A hyperbola

Question 60

What is the slope of the line with the equation y = 2x + 3?

Accepted Answer

2

Answer

-2

Answer

3

Answer

-3

Question 61

What is the range of the function f(x) = 2^x?

Accepted Answer

All positive numbers

Answer

All negative numbers

Answer

All real numbers

Answer

Only 2

Question 62

Determine the domain of the function h(x) = sqrt(x + 2).

Accepted Answer

x > -2

Answer

x < -2

Answer

x > 0

Answer

x < 0

Question 63

What is the period of the function f(x) = sin(2x)?

Accepted Answer

2π

Answer

π

Answer

π/2

Answer

4π

Question 64

Determine the inverse function of f(x) = x^2 for x ≥ 0.

Accepted Answer

g(x) = sqrt(x)

Answer

h(x) = -sqrt(x)

Answer

k(x) = x^2

Answer

l(x) = -x^2