Functions in Math: Interactive Quizzes and Learning Resources

Question 1

In a linear function's graph, how do the slope and y-intercept relate to its equation?

Accepted Answer

The slope shows the 'x' coefficient, and the y-intercept shows the constant term.

Answer

The slope and y-intercept have no connection to the equation.

Answer

The y-intercept shows the 'x' coefficient, and the slope shows the constant term.

Question 2

Sofia has 50 feet of fencing to create a rectangular garden. Express the area of the garden as a function of its length.

Accepted Answer

A = (50 - 2x)x

Answer

A = 50x

Answer

A = 25x

Answer

A = x^2

Question 3

Which of the following is NOT a characteristic of functions?

Accepted Answer

The domain and range of a function can be any sets of numbers.

Answer

A function has a unique output for each input within its domain.

Answer

Functions can be represented visually.

Answer

Functions can be expressed using equations.

Question 4

Which equation represents a linear function?

Accepted Answer

y = 2x + 3

Answer

y = x^2 + 2x - 1

Answer

y = sin(x)

Question 5

Which graph represents the function y = x^2 - 2x + 1?

Accepted Answer

A parabola opening upwards with its vertex at (1, 0)

Answer

A straight line with a positive slope

Answer

A parabola opening downwards with its vertex at (0, 1)

Answer

A circle with a radius of 1

Question 6

Which of the following is NOT a defining characteristic of functions?

Accepted Answer

A function can have multiple inputs for a single output.

Answer

A function assigns each input to exactly one output.

Answer

The domain of a function is the set of all possible inputs.

Answer

The range of a function is the set of all possible outputs.

Question 7

Identify the relation that represents a function. Remember, each input (x-value) must correspond to exactly one output (y-value).

Accepted Answer

{(1, 1), (2, 2), (3, 4), (4, 5)}

Answer

{(1, 2), (2, 3), (3, 4), (3, 5)}

Answer

{(2, 1), (2, 3), (-1,1), (0,1)}

Answer

{(2, 0), (2, 1), (3, 1), (3, 2)}

Question 8

Which property is NOT true for a function?

Accepted Answer

Multiple outputs are possible for a single input.

Answer

Each input has exactly one output.

Answer

The domain includes all possible inputs.

Answer

The range contains all possible outputs.

Question 9

Which of the following is NOT a property of a function?

Accepted Answer

A function can have multiple outputs for a single input.

Answer

The domain of a function includes all possible input values.

Answer

The range of a function consists of all possible output values.

Question 10

Which equation represents a quadratic function?

Accepted Answer

y = x² + 2x + 1

Answer

y = x³ - 3x + 2

Answer

y = 2x + 5

Answer

y = √x

Question 11

What is a defining characteristic of a function?

Accepted Answer

For every input, there is exactly one output.

Answer

The output can be any number.

Answer

The graph of a function is always a straight line.

Answer

The same input can produce different outputs.

Question 12

Which graph represents the quadratic function f(x) = -x^2 + 4?

Accepted Answer

A parabola opening downward with a vertex at (0, 4)

Answer

A parabola opening upward with a vertex at (0, 4)

Answer

A line with a slope of -1 and a y-intercept of 4

Answer

A circle with a radius of 2 and a center at (0, 0)

Question 13

Which of the following relations is NOT a function? Select the relation and explain why it is not a function.

Accepted Answer

{(1, 2), (1, 3), (3, 5)}

Answer

{(2, 3), (4, 5), (6, 7)}

Answer

{(1, 1), (2, 2), (3, 3)}

Question 14

Which characteristic is not a defining property of functions?

Accepted Answer

The graph of a function may have points where it crosses itself.

Answer

A function assigns a unique output value to each input value.

Answer

The domain of a function includes all possible input values.

Question 15

Which of the following is a function? A relation that assigns to each element of a set exactly one element of another set.

Accepted Answer

The relation {(1, 2), (2, 4), (3, 6)}

Answer

The set of all even numbers

Answer

The set of all prime numbers less than 10

Answer

The relation {(1, 2), (1, 4), (2, 6)}

Question 16

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

Accepted Answer

A straight line

Answer

A parabola

Answer

A circle

Answer

An ellipse

Question 17

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

Accepted Answer

y = ax^2 + bx + c

Answer

y = mx + b

Answer

y = e^x

Answer

y = log x

Question 18

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 circle

Question 19

Which of the following is a property of increasing functions?

Accepted Answer

The graph rises from left to right.

Answer

The graph falls from left to right.

Answer

The graph is constant.

Answer

The graph has a maximum.

Question 20

Which of the following is the domain of the function f(x) = 1/x?

Accepted Answer

All real numbers except 0

Answer

All real numbers including 0

Answer

All positive real numbers

Answer

All negative real numbers

Question 21

Which of the following is the inverse of the function f(x) = 2x + 1?

Accepted Answer

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

Answer

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

Answer

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

Answer

f^-1(x) does not exist

Question 22

Which of the following equations represents a linear function?

Accepted Answer

f(x) = 3x - 5

Answer

f(x) = x^2 + 1

Answer

f(x) = 2^x

Answer

f(x) = sin(x)

Question 23

What is the slope of the line represented by the equation y = 2x - 3?

Accepted Answer

2

Answer

-3

Answer

1/2

Answer

-1/2

Question 24

Which of the following graphs represents a quadratic function?

Accepted Answer

A parabola

Answer

A straight line

Answer

A circle

Answer

An ellipse

Question 25

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

Accepted Answer

(2, -1)

Answer

(2, 1)

Answer

(-2, 1)

Answer

(-2, -1)

Question 26

Which of the following functions is an exponential function?

Accepted Answer

f(x) = 3^x

Answer

f(x) = x + 5

Answer

f(x) = sqrt(x)

Answer

f(x) = 1/x

Question 27

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

Accepted Answer

All real numbers except 2

Answer

All real numbers

Answer

All real numbers less than 2

Answer

All real numbers greater than 2

Question 28

What is the inverse function of f(x) = 2x + 1?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 29

Which of the following is a composite function?

Accepted Answer

f(g(x))

Answer

f(x) + g(x)

Answer

f(x) - g(x)

Answer

f(x) * g(x)

Question 30

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

Accepted Answer

All non-negative real numbers

Answer

All real numbers

Answer

All positive real numbers

Answer

All negative real numbers

Question 31

Which equation represents a linear function?

Accepted Answer

y = 2x + 3

Answer

y = x^2

Answer

y = cos(x)

Answer

y = 1/(x-1)

Question 32

What is the slope of the linear function represented by the equation y = -2x + 5?

Accepted Answer

-2

Answer

2

Answer

5

Answer

-5

Question 33

Which of the following is the graph of the quadratic function y = x^2 - 4?

Accepted Answer

A parabola that opens downwards

Answer

A parabola that opens upwards

Answer

A circle

Answer

A straight line

Question 34

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

Accepted Answer

x ≥ 0

Answer

All real numbers

Answer

x < 0

Answer

x ≠ 0

Question 35

Which of the following functions is an inverse function of f(x) = 2x + 1?

Accepted Answer

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

Answer

g(x) = 1/(2x + 1)

Answer

g(x) = -2x - 1

Answer

g(x) = 2x - 1

Question 36

Which of the following is NOT a type of function?

Accepted Answer

Polynomial

Answer

Linear

Answer

Quadratic

Answer

Exponential

Question 37

Identify the equation representing a linear function:

Accepted Answer

y = 2x + 1

Answer

y = x^2

Answer

y = e^x

Answer

y = sin(x)

Question 38

Find the slope of the line described by the equation y = -3x + 2.

Accepted Answer

-3

Answer

2

Answer

1

Answer

0

Question 39

Which graph represents a quadratic function?

Accepted Answer

A parabola

Answer

A straight line

Answer

An exponential curve

Answer

A trigonometric wave

Question 40

Which of the following is NOT a property of an exponential function?

Accepted Answer

The y-intercept is always (0, 1).

Answer

The graph increases rapidly.

Answer

The domain is all real numbers.

Answer

The range is all positive numbers.

Question 41

Determine the rate of growth of the exponential function y = 2^x.

Accepted Answer

2

Answer

1

Answer

4

Answer

8

Question 42

Which transformation shifts a function graph up by 2 units?

Accepted Answer

f(x) + 2

Answer

f(x - 2)

Answer

f(x + 2)

Answer

f(x) - 2

Question 43

Determine the domain and range of the function f(x) = 2x - 1.

Accepted Answer

Domain: All real numbers; Range: All real numbers

Answer

Domain: Non-negative real numbers; Range: All real numbers

Answer

Domain: Positive real numbers; Range: Values greater than -1

Question 44

Which graph accurately represents the function y = x² - 4?

Accepted Answer

Parabola opening upwards with vertex at (0, -4)

Answer

Parabola opening downwards with vertex at (0, -4)

Answer

Straight line with slope 2 and y-intercept -4

Answer

Circle with center at (0, -4)

Question 45

What is the equation of the line that passes through the points (2, 5) and (4, 11)?

Accepted Answer

y = 3x - 1

Answer

y = x + 3

Answer

y = 2x + 1

Answer

y = 4x + 2

Question 46

Which graph represents a quadratic function that has a minimum value?

Accepted Answer

A parabola opening downward.

Answer

A parabola opening upward.

Answer

A line with a positive slope.

Answer

A line with a negative slope.

Question 47

Which of the following transformations would move the graph of the function f(x) = x^2 to the left by 3 units?

Accepted Answer

f(x - 3)

Answer

f(x + 3)

Answer

f(3x)

Answer

f(x/3)

Question 48

What is the domain of the function f(x) = sqrt(x - 2)?

Accepted Answer

All real numbers greater than or equal to 2

Answer

All real numbers less than or equal to 2

Answer

All real numbers

Answer

Only the number 2

Question 49

Which of the following graphs represents a function that is both increasing and concave upward?

Accepted Answer

A parabola opening upward

Answer

A parabola opening downward

Answer

A line with a positive slope

Answer

A line with a negative slope

Question 50

To move the graph of the function  y = x² - 4x + 3  up by 2 units, which transformation should be applied?

Accepted Answer

y = x² - 4x + 5

Answer

y = x² - 4x + 1

Answer

y = (x - 2)² - 4x + 3

Answer

y = 2(x² - 4x + 3)

Question 51

For the function f(x) = 3x^2 - 2x + 1, find the coordinates of the vertex of its graph.

Accepted Answer

(-1/3, 2/3)

Answer

(1/3, -2/3)

Answer

(0, 1)

Answer

(3, 26)

Question 52

Which type of function is represented by the equation f(x) = |x - 2| + 3?

Accepted Answer

Absolute Value Function

Answer

Linear Function

Answer

Quadratic Function

Question 53

Consider the linear function f(x) = -3x + 2 and the exponential function g(x) = 2^x. Which statement best describes the contrasting growth patterns of these functions?

Accepted Answer

f(x) grows linearly, while g(x) grows exponentially.

Answer

Both f(x) and g(x) grow linearly.

Answer

Both f(x) and g(x) grow exponentially.

Answer

f(x) grows exponentially, while g(x) grows linearly.

Question 54

What is a defining characteristic of linear functions?

Accepted Answer

Their graphs are straight lines.

Answer

Their graphs always increase.

Answer

Their graphs have a U-shape.

Question 55

Identify the function that is NOT a transformation of the parent function f(x) = x². Explain your reasoning.

Accepted Answer

j(x) = x³

Answer

g(x) = (x + 3)² - 2

Answer

h(x) = -2x²

Question 56

Which of the following is a key property of a function?

Accepted Answer

Each input value corresponds to exactly one output value.

Answer

The function can be represented by an equation or graph only.

Answer

The range can have repeated values.

Answer

The domain and range are sets of numbers only.

Question 57

Which of the following graphs represents a linear function?

Accepted Answer

A straight line

Answer

A curved figure that resembles a tilted letter 'V'

Answer

A curve that does not intersect itself

Answer

A closed figure with a curved boundary

Question 58

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

Accepted Answer

All real numbers

Answer

Negative real numbers only

Answer

Integers only

Answer

Positive real numbers only

Question 59

Identify the type of function represented by the equation y = x^2 + 3x - 5.

Accepted Answer

Quadratic

Answer

Cubic

Answer

Linear

Answer

Exponential

Question 60

Which of the following is NOT a property of functions?

Accepted Answer

The output can be any real number.

Answer

Each input value corresponds to exactly one output value.

Answer

Functions can be expressed as equations, graphs, or tables.

Answer

The domain and range are sets of values.

Question 61

Find the y-intercept of the function f(x) = -2x + 5.

Accepted Answer

5

Answer

0

Answer

2

Answer

-2

Question 62

Which of the following is the equation of a line parallel to the x-axis?

Accepted Answer

y = 2

Answer

y = x + 2

Answer

y = x^2

Answer

y = x

Question 63

Find the range of the function h(x) = |x|.

Accepted Answer

y ≥ 0

Answer

y > 0

Answer

y ≤ 0

Answer

y < 0

Question 64

Which of the following functions represents an inverse variation relationship?

Accepted Answer

f(x) = 1/x

Answer

f(x) = x^3

Answer

f(x) = x^2

Answer

f(x) = 2x