Functions: Interactive Learning Quizzes for Year 12 Mathematics

Question 1

Identify the period of the function y = cos(3x).

Accepted Answer

π/3

Answer

1

Answer

π

Answer

2π

Question 2

Which of the following transformations does NOT affect the graph of a function?

Accepted Answer

Rotation about the origin

Answer

Translation

Answer

Reflection

Answer

Scaling

Question 3

The graph of the function f(x) = x^2 is a:

Accepted Answer

Quadratic function

Answer

Linear function

Answer

Cubic function

Answer

Exponential function

Question 4

Which of the following functions has a range of all real numbers?

Accepted Answer

f(x) = |x|

Answer

f(x) = x^3

Answer

f(x) = sin(x)

Answer

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

Question 5

Which of the following is an example of a composite function?

Accepted Answer

f(g(x))

Answer

g(f(x))

Answer

f(x) + g(x)

Answer

f(x) - g(x)

Question 6

Which of the following transformations is NOT applicable to functions?

Accepted Answer

Enlargement or reduction

Answer

Vertical translation

Answer

Horizontal translation

Answer

Reflection over the x-axis

Question 7

Which of the following functions is considered linear?

Accepted Answer

f(x) = 2x + 3

Answer

f(x) = x³ + 1

Answer

f(x) = sin(x)

Answer

f(x) = e^x

Question 8

For the function f(x) = 1 / (x - 2), the domain is:

Accepted Answer

All real numbers except 2

Answer

All real numbers except 0

Answer

All real numbers

Answer

Only positive real numbers

Question 9

Which type of function is f(x) = 3^x?

Accepted Answer

Exponential

Answer

Linear

Answer

Quadratic

Answer

Cubic

Question 10

Which of the following equations represents a linear function?

Accepted Answer

y = mx + c

Answer

y = ax² + bx + c

Answer

y = ax³ + bx² + cx + d

Answer

y = e^(mx + c)

Question 11

What is the gradient of the linear function y = 2x - 5?

Accepted Answer

2

Answer

-2

Answer

5

Answer

-5

Question 12

Which of the following graphs represents a quadratic function?

Accepted Answer

A parabola

Answer

A straight line

Answer

A circle

Answer

A hyperbola

Question 13

What is the domain of the function y = 1/x?

Accepted Answer

All real numbers except 0

Answer

All real numbers

Answer

All negative real numbers

Answer

All positive real numbers

Question 14

What is the inverse of the function y = 2x + 1?

Accepted Answer

x = (y - 1)/2

Answer

x = 2y - 1

Answer

x = 1/2y + 1

Answer

x = 2/y + 1

Question 15

Which of the following correctly represents the equation of a linear function?

Accepted Answer

f(x) = mx + c

Answer

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

Answer

f(x) = a(x - h)^2 + k

Answer

f(x) = a/(x - h) + k

Question 16

Find the gradient of the line with the equation y = 2x - 5.

Accepted Answer

2

Answer

-5

Answer

1

Answer

-2

Question 17

Determine the axis of symmetry of the parabola with the equation y = x^2 - 4x + 3.

Accepted Answer

x = 2

Answer

x = -2

Answer

y = 2

Answer

y = -2

Question 18

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

Accepted Answer

y > 0

Answer

y >= 1

Answer

y <= 1

Answer

y < 0

Question 19

Determine the inverse of the function 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) = -2x - 1

Question 20

Find the composite function of f(x) = x^2 and g(x) = x + 1.

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 21

Identify the domain restriction for the function f(x) = 1/x.

Accepted Answer

x ≠ 0

Answer

x = 0

Answer

x < 0

Answer

x > 0

Question 22

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

Accepted Answer

A straight line

Answer

A parabola

Answer

A circle

Answer

A hyperbola

Question 23

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

Accepted Answer

All real numbers except 2

Answer

All real numbers

Answer

All positive real numbers

Answer

All negative real numbers

Question 24

Which transformation would translate 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(x) - 3

Answer

f(x + 3)^2

Question 25

What is the composition of the functions f(x) = x^2 and g(x) = x-1?

Accepted Answer

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

Answer

f(g(x)) = x^3 - x^2

Answer

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

Answer

g(f(x)) = x^3 - x

Question 26

Determine the equation of the line that passes through points (2, 3) and (5, 7).

Accepted Answer

y = 2x + 1

Answer

y = x + 1

Answer

y = x - 1

Answer

y = 2x - 1

Question 27

Which transformation would shift the graph of y = x^3 two units to the right?

Accepted Answer

y = (x + 2)^3

Answer

y = (x - 2)^3

Answer

y = x^3 + 2

Answer

y = x^3 - 2

Question 28

Which function is a cubic function?

Accepted Answer

y = x^3 - 3x^2 + 2x + 1

Answer

y = x^2 + 2x - 1

Answer

y = sqrt(x)

Answer

y = e^x

Question 29

Determine the equation of the horizontal asymptote of the function f(x) = (x^2 + 1) / (x - 1).

Accepted Answer

y = 1

Answer

y = -1

Answer

y = x

Answer

y = -x

Question 30

Which of the following types of functions is NOT covered in this unit?

Accepted Answer

Exponential

Answer

Linear

Answer

Quadratic

Answer

Cubic

Question 31

In the linear function y = mx + c, what does 'm' represent?

Accepted Answer

Slope

Answer

Y-intercept

Answer

X-intercept

Answer

Domain

Question 32

Which transformation would shift the graph of y = x^2 to the left by 3 units?

Accepted Answer

y = (x - 3)^2

Answer

y = x^2 - 3

Answer

y = x^2 + 3

Answer

y = 3x^2

Question 33

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

Accepted Answer

All real numbers except for 2

Answer

All real numbers except for 0

Answer

All real numbers

Answer

The empty set

Question 34

What is the range of the function f(x) = |x - 1|?

Accepted Answer

All real numbers greater than or equal to 0

Answer

All real numbers

Answer

All real numbers greater than or equal to 1

Answer

All real numbers less than or equal to 1

Question 35

Which of the following is the equation of a linear function with a gradient of 2 and a y-intercept of -1?

Accepted Answer

y = 2x - 1

Answer

y = -2x + 1

Answer

y = 2x + 1

Answer

y = -2x - 1

Question 36

What is the vertex of the quadratic function f(x) = x^2 - 4x + 3?

Accepted Answer

(2, -1)

Answer

(2, -5)

Answer

(2, 1)

Answer

(2, 5)

Question 37

Which of the following transformations will 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 38

What is the inverse of the function 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) does not exist

Question 39

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

Accepted Answer

x > 1

Answer

x < 1

Answer

x ≥ 1

Answer

x ≤ 1

Question 40

Given a linear function with a slope of 2 and a y-intercept of -3, what is its equation?

Accepted Answer

y = 2x - 3

Answer

y = 2x + 3

Answer

y = -2x + 3

Answer

y = -2x - 3

Question 41

Specify the domain of the function f(x) = 1/(x - 2).

Accepted Answer

All real numbers except 2

Answer

All real numbers

Answer

The set of positive real numbers

Answer

The set of negative real numbers

Question 42

Identify the range of the function f(x) = |x + 1|.

Accepted Answer

All real numbers greater than or equal to 0

Answer

All real numbers less than or equal to 0

Answer

The set of positive real numbers

Answer

The set of negative real numbers

Question 43

Which of the following is a transformation that will move the graph of y = x^2 up 3 units?

Accepted Answer

y = x^2 + 3

Answer

y = x^2 - 3

Answer

y = 3x^2

Answer

y = (x + 3)^2

Question 44

Which of the following transformations will flip the graph of y = f(x) over the y-axis?

Accepted Answer

y = f(-x)

Answer

y = -f(-x)

Answer

y = f(x) + 1

Answer

y = f(x-1)

Question 45

Which of the following is the standard equation of a linear function?

Accepted Answer

y = ax + b

Answer

y = ax^2 + bx + c

Answer

y = ax^3 + bx^2 + cx + d

Answer

y = a/x + b/x^2

Question 46

What is the gradient of the straight line represented by y = 2x + 5?

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 47

What is the y-intercept of the straight line represented by y = -3x + 2?

Accepted Answer

2

Answer

-1

Answer

1

Answer

3

Question 48

What is the domain of the rational function y = 1/x?

Accepted Answer

All real numbers except 0

Answer

All real numbers

Answer

Negative real numbers only

Answer

Positive real numbers only

Question 49

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

Accepted Answer

A parabola opening upwards

Answer

A straight line

Answer

A parabola opening downwards

Answer

A circle

Question 50

Which of the following is the equation of the transformation of the quadratic function y = x^2 that shifts it 3 units to the left?

Accepted Answer

y = (x - 3)^2

Answer

y = (x + 3)^2

Answer

y = x^2 + 3

Answer

y = x^2 - 3

Question 51

Which of the following is the inverse of the linear function y = 2x + 1?

Accepted Answer

y = (x - 1)/2

Answer

y = 2x - 1

Answer

y = x^2 - 1

Answer

y = 1/x

Question 52

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

Accepted Answer

y = 2x + 1

Answer

y = x^2 - 2

Answer

y = 1/x

Answer

y = sin(x)

Question 53

Which of the following is not a transformation of a function?

Accepted Answer

Rotation

Answer

Translation

Answer

Reflection

Answer

Scaling

Question 54

The graph of the function f(x) = -x^3 is:

Accepted Answer

A cubic function opening downwards

Answer

A parabola opening downwards

Answer

A parabola opening upwards

Answer

A cubic function opening upwards

Question 55

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

Accepted Answer

All real numbers except 2

Answer

All real numbers

Answer

All positive real numbers

Answer

All negative real numbers

Question 56

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

Accepted Answer

[0, ∞)

Answer

[-1, ∞)

Answer

(0, ∞)

Answer

[-∞, ∞)

Question 57

Which of the following functions is even?

Accepted Answer

f(x) = |x|

Answer

f(x) = x^3

Answer

f(x) = x^2-1

Answer

f(x) = sin(x)

Question 58

The inverse of the function f(x) = 2x+1 is:

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 59

The derivative of the function f(x) = x^3 - 2x^2 + 1 is:

Accepted Answer

3x^2 - 4x

Answer

3x^2 + 4x

Answer

x^3 - 4x^2

Answer

x^3 + 4x^2

Question 60

Find the gradient of the line with equation y = 3x - 5. (GCSE Mathematics)

Accepted Answer

3

Answer

-5

Answer

5

Answer

-3

Question 61

Which of the following is the equation of the quadratic function with vertex (2, -3) and y-intercept (0, 4)? (GCSE Mathematics)

Accepted Answer

y = (x - 2)^2 - 3

Answer

y = (x + 2)^2 - 3

Answer

y = (x - 2)^2 + 3

Answer

y = (x + 2)^2 + 3

Question 62

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

Accepted Answer

All real numbers except x = 2

Answer

All real numbers except x = 0

Answer

All real numbers

Answer

Only x = 2

Question 63

Which of the following functions is even? (GCSE Mathematics)

Accepted Answer

f(x) = x^2 - 4

Answer

f(x) = x^3 + 2x

Answer

f(x) = x^3 - x

Answer

f(x) = x^2 + 3x

Question 64

Which of the following equations represents a linear function?

Accepted Answer

y = 2x + 1

Answer

y = x^2 - 1

Answer

y = (x + 1)^3

Answer

y = 1/(x-2)