Graphs: Interactive Learning Quizzes for Year 11 Mathematics

Question 1

The graph of the quadratic function y = x^2 - 4x + 3 has its turning point at:

Accepted Answer

(2, 5)

Answer

(2, -5)

Answer

(3, 5)

Answer

(3, -5)

Question 2

Identify the gradient of the line represented by the equation y = -2x + 5.

Accepted Answer

-2

Answer

2

Answer

5

Answer

-5

Question 3

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

Accepted Answer

[Image of a parabola opening downwards with vertex at (-2, 1)]

Answer

[Image of a parabola opening upwards with vertex at (-2, 1)]

Answer

[Image of a straight line with negative gradient]

Answer

[Image of a straight line with positive gradient]

Question 4

Find the equation of the straight line that has a slope of 2 and a y-intercept of -3.

Accepted Answer

y = 2x - 3

Answer

y = -2x - 3

Answer

y = 3x - 2

Answer

y = -3x - 2

Question 5

Which of the following graphs represents a quadratic function with a negative leading coefficient?

Accepted Answer

A parabola opening downwards

Answer

A parabola opening upwards

Answer

A straight line with a positive slope

Answer

A straight line with a negative slope

Question 6

Identify the key feature of the graph of a linear function that indicates the direction of the line

Accepted Answer

Slope

Answer

Y-intercept

Answer

Vertex

Answer

Domain

Question 7

Which of the following is a property of quadratic functions?

Accepted Answer

They have a maximum or minimum point

Answer

Their graphs are always concave up

Answer

They have a constant slope

Answer

They are always increasing

Question 8

Which equation represents a line with a gradient of 2 and a y-intercept of -3?

Accepted Answer

y = 2x - 3

Answer

y = 3x - 2

Answer

y = -2x - 3

Answer

y = -3x - 2

Question 9

Which transformation moves the parabola y = x^2 left by 2 units?

Accepted Answer

y = (x - 2)^2

Answer

y = (x + 2)^2

Answer

y = x^2 - 2

Answer

y = x^2 + 2

Question 10

Determine the gradient of the line perpendicular to y = 2x + 3.

Accepted Answer

-1/2

Answer

1/2

Answer

2

Answer

-2

Question 11

Find the range of the function y = |x| - 1.

Accepted Answer

y ≥ -1

Answer

y ≤ -1

Answer

y ≥ 1

Answer

y ≤ 1

Question 12

Determine the domain of the function y = 1/x.

Accepted Answer

All real numbers except 0

Answer

All real numbers

Answer

x ≥ 0

Answer

x ≤ 0

Question 13

Identify the graph of the linear function f(x) = 2x + 1:

Accepted Answer

Graph A: A line with a steep positive slope and a low y-intercept

Answer

Graph B: A line with a shallow negative slope and a high y-intercept

Answer

Graph C: A parabola opening upwards with a vertex at (0, 1)

Answer

Graph D: A horizontal line passing through the y-axis at y = 2

Question 14

Determine the equation of the linear function represented by the graph with 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

For the function y = 1 / x, find its domain.

Accepted Answer

All real numbers excluding 0

Answer

All real numbers

Answer

All non-negative real numbers

Answer

All positive real numbers

Question 16

Which of the following graphs depicts the inequality y > 2x - 1?

Accepted Answer

A line with a slope of 2 and y-intercept of 1, with the area above the line shaded

Answer

A line with a slope of 2 and y-intercept of 1, with the area below the line shaded

Answer

A line with a slope of -2 and y-intercept of 1, with the area above the line shaded

Answer

A line with a slope of -2 and y-intercept of 1, with the area below the line shaded

Question 17

Which of the following graphs represents the inverse of the function y = x^2 + 1?

Accepted Answer

y = √(x + 1)

Answer

y = x^2 - 1

Answer

y = -x^2 + 1

Answer

y = √(x - 1)

Question 18

The range of the graph of the function f(x) = 2|x - 1| - 3 is:

Accepted Answer

y ≥ -3

Answer

y ≤ -3

Answer

y ≤ 1

Answer

y ≥ 1

Question 19

Find the equation of a linear function with a gradient of 2 and a y-intercept of 3.

Accepted Answer

y = 2x + 3

Answer

y = 3x + 2

Answer

y = 2x - 3

Answer

y = 3x - 2

Question 20

Identify the y-intercept of the graph of the quadratic function f(x) = x^2 - 4x + 3.

Accepted Answer

3

Answer

-3

Answer

0

Answer

4

Question 21

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

Accepted Answer

y = (x - 2)^2

Answer

y = (x + 2)^2

Answer

y = x^2 + 2

Answer

y = x^2 - 2

Question 22

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

Accepted Answer

All real numbers except 2

Answer

All real numbers

Answer

All negative real numbers

Answer

All positive real numbers

Question 23

Determine the range of the function f(x) = |x - 3|.

Accepted Answer

All non-negative real numbers

Answer

All real numbers less than or equal to 3

Answer

All real numbers greater than or equal to 3

Answer

All negative real numbers

Question 24

Which of the following is the equation of a line with a slope of 2 and a y-intercept of -1?

Accepted Answer

y = 2x - 1

Answer

y = -x - 2

Answer

y = x + 2

Answer

y = -2x + 1

Question 25

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

Accepted Answer

[2, ∞)

Answer

(-∞, 2]

Answer

[0, ∞)

Answer

(-∞, ∞)

Question 26

Which of the following is the equation of the line passing through the points (2, 5) and (4, 9)?

Accepted Answer

y = 2x + 1

Answer

y = 4x + 5

Answer

y = x + 3

Answer

y = 3x - 1

Question 27

What is the slope of the line represented by the equation y = -3x + 5?

Accepted Answer

-3

Answer

1

Answer

3

Answer

-5

Question 28

Which of the following graphs represents the quadratic function f(x) = x^2 - 4x + 3?

Accepted Answer

A parabola opening upward with vertex at (2, -1)

Answer

A straight line with slope 2

Answer

A parabola opening downward with vertex at (2, -1)

Answer

A circle with radius 2

Question 29

What is the y-intercept of the graph of the function g(x) = -2x^2 + 4x - 1?

Accepted Answer

-1

Answer

2

Answer

-2

Answer

1

Question 30

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

Accepted Answer

All real numbers except 2

Answer

The interval (0, 2)

Answer

All real numbers

Question 31

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

Accepted Answer

The interval [-1, ∞)

Answer

The interval (0, ∞)

Answer

The interval (-1, ∞)

Answer

The interval (-∞, -1)

Question 32

Which of the following graphs represents a one-to-one function?

Accepted Answer

A graph that passes the horizontal line test

Answer

A graph that is decreasing

Answer

A graph that is increasing

Answer

A graph that is symmetric about the x-axis

Question 33

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) = x^2 + 1

Answer

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

Answer

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

Question 34

Which of the following 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^4 + 1

Answer

f(g(x)) = x^3 + 1

Answer

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

Question 35

Which of the following is the equation of the graph of a linear function that passes through the points (2, 5) and (-1, 1)?

Accepted Answer

y = 2x + 3

Answer

y = -2x + 1

Answer

y = x + 5

Answer

y = 3x - 2

Question 36

What is the y-intercept of the graph of the function f(x) = 2x^2 - 3x + 1?

Accepted Answer

1

Answer

2

Answer

0

Answer

-3

Question 37

Which of the following graphs represents the function f(x) = (x - 2)^2 + 1?

Accepted Answer

A parabola that shifts 2 units to the right and 1 unit up.

Answer

A parabola that shifts 2 units to the right and 1 unit down.

Answer

A parabola that shifts 2 units to the left and 1 unit up.

Question 38

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

Accepted Answer

x ≥ -2

Answer

x ≤ -2

Answer

x < -2

Answer

x > -2

Question 39

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

Accepted Answer

A line that passes through the origin with a slope of 1/2.

Answer

A parabola that opens upward.

Answer

A line that passes through the origin with a slope of 2.

Question 40

What is the slope of the tangent line to the graph of the function f(x) = x^3 - 2x^2 + 1 at the point (1, 0)?

Accepted Answer

1

Answer

0

Answer

2

Answer

-1

Question 41

Which of the following graphs represents the function f(x) = |x - 1|?

Accepted Answer

A V-shaped graph with a vertex at (1, 0).

Answer

A parabola that opens upward.

Answer

A U-shaped graph with a vertex at (1, 0).

Answer

A line that passes through the origin with a slope of 1.

Question 42

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

Accepted Answer

(2, 1)

Answer

(-2, 1)

Answer

(2, -1)

Answer

(1, 2)

Question 43

Which of the following inequalities is represented by the graph that shows the shaded region below the line y = 2x - 1?

Accepted Answer

y < 2x - 1

Answer

y ≤ 2x - 1

Answer

y ≥ 2x - 1

Answer

y > 2x - 1