Functions: Master the Basics with Interactive Quizzes

Question 1

Which graph represents the function f(x) = |x|?

Accepted Answer

A V-shaped graph symmetrical about the y-axis

Answer

A straight line with a positive slope

Answer

A parabola opening upwards

Answer

A circle centered at the origin

Question 2

Identify the range of the function f(x) = x^2 - 2

Accepted Answer

All non-negative numbers

Answer

All positive numbers

Answer

All numbers greater than or equal to -2

Answer

All real numbers

Question 3

Which function has an inverse function?

Accepted Answer

f(x) = 1/x

Answer

f(x) = x^2

Answer

f(x) = |x|

Answer

f(x) = 2x + 1

Question 4

Which graph corresponds to the function f(x) = -x + 2?

Accepted Answer

[Image of a straight line with a slope of -1 and a y-intercept of 2]

Answer

[Image of a parabola]

Answer

[Image of a circle]

Answer

[Image of a hyperbola]

Question 5

Identify the characteristic of a function that is incorrect:

Accepted Answer

The function can be expressed as an inequality.

Answer

Each input corresponds to exactly one output.

Answer

The relationship between input and output is predictable.

Answer

The output can take on any value within the range.

Question 6

Determine the inverse function of f(x) = (x + 1) / 2:

Accepted Answer

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

Answer

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

Answer

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

Answer

f^-1(x) does not exist.

Question 7

Identify the graph of the function: f(x) = 2x^2 - 4x + 3:

Accepted Answer

[Image of a parabola opening upwards]

Answer

[Image of a parabola opening downwards]

Answer

[Image of a linear function]

Answer

[Image of a sinusoidal function]

Question 8

Determine the transformation that shifts the graph of f(x) = x^3 to the right by 2 units:

Accepted Answer

f(x) -> f(x + 2)

Answer

f(x) -> f(x - 2)

Answer

f(x) -> f(2x)

Answer

f(x) -> f(x) / 2

Question 9

Identify the domain of the function f(x) = 1/(x - 3)?

Accepted Answer

{x | x ≠ 3}

Answer

{x | x < 0}

Answer

{x | x > 0}

Answer

{x | x ≠ 0}

Question 10

Which of the following functions is even?:

Accepted Answer

f(x) = |x|

Answer

f(x) = x^2 + 1

Answer

f(x) = x^2 - 1

Answer

f(x) = x^3

Question 11

Which of the following is a discontinuity in the function f(x) = 1/x? :

Accepted Answer

x = 0

Answer

x = 1

Answer

x = -1

Answer

x = 2

Question 12

Identify the period of the function f(x) = sin(2x):

Accepted Answer

2π

Answer

π

Answer

π/2

Answer

4π

Question 13

Find the domain of the function f(x) = 1/(x-5).

Accepted Answer

{x | x ≠ 5}

Answer

{x | x > 5}

Answer

{x | x < 5}

Answer

{x | x ∈ ℝ}

Question 14

Find the range of the function f(x) = -x^2 + 4.

Accepted Answer

{y | y ≤ 4}

Answer

{y | y > 4}

Answer

{y | y < 4}

Answer

{y | y ∈ ℝ}

Question 15

Which of the following is a composite function?

Accepted Answer

f(x) = g(h(x))

Answer

f(x) = x^2

Answer

f(x) = sin(x)

Answer

f(x) = x + 1

Question 16

Find the derivative of the function f(x) = 2x^3 + 5x - 1.

Accepted Answer

6x^2 + 5

Answer

2x^2 + 5

Answer

6x + 5

Answer

x^2 + 5x - 1

Question 17

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

Accepted Answer

Magnitude

Answer

Domain

Answer

Range

Answer

Inverse functions

Question 18

For the function f(x) = sqrt(x-1), what is its domain?

Accepted Answer

x ≥ 1

Answer

x < 1

Answer

x > 0

Answer

All real numbers

Question 19

Which of the equations represents the inverse function of g(x) = 2x + 1?

Accepted Answer

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

Answer

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

Answer

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

Answer

g^-1(x) does not exist

Question 20

Determine the range of the function f(x) = |x-2|.

Accepted Answer

y ≥ 0

Answer

y < 0

Answer

y > 2

Answer

All real numbers

Question 21

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

Accepted Answer

2

Answer

1

Answer

3

Answer

6

Question 22

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

Accepted Answer

f(x-2)

Answer

f(x+2)

Answer

f(2x)

Answer

f(x/2)

Question 23

Find the local minimum of the function f(x) = x^3 - 3x^2 + 2.

Accepted Answer

x = -1

Answer

x = 1

Answer

x = 0

Answer

The function has no local minimum

Question 24

Which of the following properties is NOT exclusive to functions?

Accepted Answer

The graph forms a straight line

Answer

Each input corresponds to exactly one output

Answer

The relation can be represented by an equation

Answer

The domain and range are sets of real numbers

Question 25

What is the domain of the function g(x) = √(x + 3)?

Accepted Answer

x ≥ -3

Answer

x < -3

Answer

x > -3

Answer

All real numbers

Question 26

Precise Question: Determine the equation of the asymptote of the function f(x) = (x + 2)/(x - 1).

Accepted Answer

Clear Option D: x = -1

Answer

Clear Option A: y = 1

Answer

Clear Option B: y = -1

Answer

Clear Option C: x = 1

Question 27

What is the solution to the equation f(x) = g(x) called?

Accepted Answer

Intersection

Answer

Domain

Answer

Range

Answer

Function

Question 28

Which transformation shifts the graph of f(x) = x² to the left by 3 units?

Accepted Answer

f(x) = (x-3)²

Answer

f(x) = (x+3)²

Answer

f(x) = x² + 3

Answer

f(x) = x² - 3

Question 29

Identify the domain of the function f(x) = log₂(x - 1).

Accepted Answer

[1, ∞)

Answer

[-∞, ∞)

Answer

[0, ∞)

Answer

(1, ∞)

Question 30

Which function is periodic?

Accepted Answer

f(x) = sin(x)

Answer

f(x) = x³

Answer

f(x) = e^x

Answer

f(x) = log₂(x)

Question 31

Determine the amplitude of the graph of the function f(x) = 2sin(3x).

Accepted Answer

2

Answer

1

Answer

3

Answer

6

Question 32

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

Accepted Answer

The output is not uniquely determined by the input.

Answer

The input is taken from a specific domain.

Answer

The output is within a specific range.

Question 33

Find the domain of the function f(x) = √(x - 2):

Accepted Answer

[2, ∞)

Answer

[0, ∞)

Answer

(-∞, ∞)

Answer

(-∞, 2]

Question 34

Which of the following is a linear function?

Accepted Answer

f(x) = 2x + 3

Answer

f(x) = 1/x

Answer

f(x) = x² - 1

Answer

f(x) = √x

Question 35

Find the equation of the function that has a graph with a y-intercept of 3 and a slope of -2:

Accepted Answer

f(x) = -2x + 3

Answer

f(x) = 2x - 3

Answer

f(x) = 2x + 3

Answer

f(x) = -2x - 3

Question 36

Which of the following is a characteristic of a function?

Accepted Answer

The output is unique for each input

Answer

The range is the set of all possible inputs

Answer

The input can repeat for different outputs

Answer

The domain is the set of all possible outputs

Question 37

Determine the domain of the function f(x) defined as f(x) = √(x-3)

Accepted Answer

[3, ∞)

Answer

[0, ∞)

Answer

(-∞, 3]

Answer

(-∞, ∞)

Question 38

Identify the graph that represents a one-to-one function:

Accepted Answer

A graph that passes the horizontal line test

Answer

A graph that is a circle

Answer

A graph that is a straight line

Answer

A graph that is a parabola

Question 39

Find the inverse of the function f(x) = 3x - 2

Accepted Answer

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

Answer

f^-1(x) does not exist

Answer

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

Answer

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

Question 40

Which of the following functions is a quadratic function?

Accepted Answer

f(x) = ax^2 + bx + c

Answer

f(x) = e^x

Answer

f(x) = log(x)

Answer

f(x) = √(x)

Question 41

Identify the trigonometric function:

Accepted Answer

f(x) = tan(x)

Answer

f(x) = √(x)

Answer

f(x) = e^x

Answer

f(x) = log(x)

Question 42

Determine the period of the function f(x) = sin(3x)

Accepted Answer

2π/3

Answer

2π

Answer

π/3

Answer

4π/3

Question 43

Which of the following statements is NOT true about functions?

Accepted Answer

The output of a function can be any real number.

Answer

Every input has exactly one output.

Answer

The input can be any real number within the function's domain.

Answer

The input and output are related by a specific rule.

Question 44

What is the domain of the function f(x) = √(x - 3)?

Accepted Answer

[3, ∞)

Answer

(-∞, ∞)

Answer

[0, ∞)

Answer

(-∞, 3]

Question 45

Which graph represents a function that is both one-to-one (injective) and onto (surjective)?

Accepted Answer

A straight line passing through the origin with a non-zero slope.

Answer

A circle centered at the origin.

Answer

An ellipse with major and minor axes of different lengths.

Answer

A parabola that opens upwards.

Question 46

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

Accepted Answer

f⁻¹(x) = (x - 1) / 2

Answer

f⁻¹(x) = x - 2

Answer

f⁻¹(x) = 1 / (2x + 1)

Answer

f⁻¹(x) = -2x + 1

Question 47

Given f(x) = 2x - 1 and g(x) = x², find (f o g)(x).

Accepted Answer

4x² - 2x - 1

Answer

2x² - 1

Answer

4x - 2

Answer

x² - 2x - 1

Question 48

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

Accepted Answer

The range can be greater than the domain.

Answer

Every input must have exactly one output.

Answer

The range is the set of all possible output values.

Answer

The domain is the set of all possible input values.

Question 49

Find the domain of the function f(x) = √(x - 2).

Accepted Answer

[2, ∞)

Answer

[-2, 2]

Answer

(0, 2]

Question 50

Graph the function f(x) = x³ - 1.

Accepted Answer

A cubic function with a negative leading coefficient, passing through the point (0, -1).

Answer

A quadratic function that opens downward and passes through the point (0, 1).

Answer

A straight line with a positive slope.

Question 51

Find the inverse of the function f(x) = 3x - 2.

Accepted Answer

f⁻¹(x) = (x + 2) / 3

Answer

f⁻¹(x) = 3x + 2

Answer

f⁻¹(x) = 1 / (3x - 2)

Answer

f⁻¹(x) does not exist.

Question 52

Which of the following functions is odd?

Accepted Answer

f(x) = x³

Answer

f(x) = x^2

Answer

f(x) = |x|

Answer

f(x) = sin(x)

Question 53

Find the range of the function f(x) = 1 / (x - 1).

Accepted Answer

(0, 1) ∪ (1, ∞)

Answer

(-∞, ∞)

Answer

(-∞, 0]

Answer

[0, 1]

Question 54

Which of the following is a horizontal asymptote of the function f(x) = (x - 1) / (x² - 1)?

Accepted Answer

y = 0

Answer

y = 1

Answer

x = 0

Answer

y = -1

Question 55

Find the equation of the line that has a slope of -2 and passes through the point (1, 3).

Accepted Answer

y = -2x + 5

Answer

y = -2x + 3

Answer

y = 2x + 1

Question 56

Which of the following is a translation of the graph of the function f(x) = x²?

Accepted Answer

g(x) = (x - 2)²

Answer

h(x) = 2x²

Answer

k(x) = √(x²)

Answer

j(x) = (x + 2)²

Question 57

Find the composition of the functions f(x) = x² - 1 and g(x) = x + 2.

Accepted Answer

h(x) = x^2 + 3x + 2

Answer

h(x) = 2x² + x + 2

Answer

h(x) = x^4 - x^2 - 1

Answer

h(x) = x^2 + x - 1