Graphs of Functions: Master the Basics with Interactive Quizzes

Question 1

Which of the following transformations shifts a graph horizontally to the right?

Accepted Answer

Translation (a, 0)

Answer

Translation (0, b)

Answer

Reflection about the x-axis

Answer

Reflection about the y-axis

Question 2

To find the y-intercept of a function, what value should you plug in for x in its equation?

Accepted Answer

0

Answer

1

Answer

The slope

Answer

The x-coordinate of any point on the graph

Question 3

Identify the graph that represents the quadratic function: f(x) = x^2 - 4

Accepted Answer

[Image of a parabola opening upwards, with vertex at (0, -4)]

Answer

[Image of a straight line with a positive slope]

Answer

[Image of a parabola opening downwards, with vertex at (0, 4)]

Question 4

Identify the function that possesses a maximum value.

Accepted Answer

f(x) = -x^2

Answer

f(x) = 1/x

Answer

f(x) = x^2

Answer

f(x) = x

Question 5

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

Accepted Answer

y ≠ 2

Answer

y = 2

Answer

y > 2

Answer

y < 2

Question 6

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

Accepted Answer

x = 1

Answer

y = -2

Answer

x = -2

Answer

y = 1

Question 7

Which of the following equations represents a linear function?

Accepted Answer

y = 2x + 1

Answer

y = |x|

Answer

y = sin(x)

Answer

y = x^2 + 2x - 1

Question 8

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

Accepted Answer

x = 1 and x = 3

Answer

x = 2 and x = -1

Answer

x = -1 and x = -3

Answer

x = -2 and x = 1

Question 9

Which of the following graphs represents the function f(x) = {x if x < 0, -x if x ≥ 0}?

Accepted Answer

A V-shaped graph with its vertex at the origin

Answer

A circle

Answer

A straight line

Answer

A U-shaped graph

Question 10

What is the graph of the linear function  *f(x) = 2x - 3*?

Accepted Answer

A straight line passing through the point (0, -3) with a slope of 2

Answer

A circle centered at (0, 0)

Answer

A parabola opening upwards

Question 11

Which transformation shifts the graph of *f(x) = x²* three units upwards?

Accepted Answer

f(x) = x² + 3

Answer

f(x) = 3x²

Answer

f(x) = x² - 3

Answer

f(x) = (x + 3)²

Question 12

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

Accepted Answer

x ≥ -3

Answer

x ≠ -3

Answer

x ∈ R

Answer

x > -3

Question 13

What is the inverse function of 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) = 1/2x - 1

Question 14

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

Accepted Answer

All real numbers except x = 2

Answer

All real numbers except x = 0

Answer

All non-negative real numbers

Answer

All real numbers

Question 15

Which equation represents the graph that is parallel to f(x) = x² and shifted upwards by 3 units?

Accepted Answer

y = x² + 3

Answer

y = 3x² + 1

Answer

y = x² - 3

Answer

y = 3x²

Question 16

Which point lies on the graph of the linear function f(x) = 2x - 3?

Accepted Answer

(1, -1)

Answer

(0, -3)

Answer

(2, 0)

Answer

(3, 3)

Question 17

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

Accepted Answer

g(x) = ±√(x) - 1

Answer

g(x) = -√(x) - 1

Answer

g(x) = √(x) + 1

Answer

g(x) = -√(x) + 1

Question 18

The domain of the function f(x) = 1 / (x - 2) is:

Accepted Answer

All real numbers except x = 2

Answer

All positive real numbers

Answer

All negative real numbers

Answer

All real numbers

Question 19

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

Accepted Answer

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

Answer

Cubic graph with vertex at (0, 0)

Answer

Quadratic graph with vertex at (0, 0)

Answer

Linear graph with slope 1 and y-intercept 1

Question 20

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

Accepted Answer

f(x) + 3

Answer

f(x) - 3

Answer

f(x + 3)

Answer

f(x - 3)

Question 21

What is the inverse of the function f(x) = log₂(x)?

Accepted Answer

g(x) = 2^x

Answer

g(x) = log₂(x)

Answer

g(x) = log₁₀(x)

Answer

g(x) = e^x

Question 22

What is the shape of the graph of the function f(x) = 1 / (x² - 4)?

Accepted Answer

Hyperbola with vertical asymptotes at x = 2 and x = -2

Answer

Linear graph with slope 1 and y-intercept 0

Answer

Quadratic graph with vertex at (0, 0)

Answer

Cubic graph with vertex at (0, 0)

Question 23

The graph of a quadratic function is a parabola. What determines whether the parabola opens upwards or downwards?

Accepted Answer

The sign of the coefficient of the x² term.

Answer

The constant term of the quadratic function.

Answer

The y-intercept of the parabola.

Answer

The x-intercepts of the parabola.

Question 24

A function is represented by the graph shown below. Is this function one-to-one?

(Insert an image of a parabola opening upwards here)

Accepted Answer

No, it fails the horizontal line test.

Answer

Yes, it is a function.

Answer

Yes, it passes the vertical line test.

Answer

No, it is a parabola.

Question 25

What is the domain of the function f(x) = 1 / (x - 4)?

Accepted Answer

All real numbers except x = 4.

Answer

All real numbers.

Answer

x = 4.

Question 26

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

Accepted Answer

A graph that opens upwards.

Answer

A graph that is a straight line.

Answer

A graph that is a circle.

Answer

A graph that opens downwards.

Question 27

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

Accepted Answer

All real numbers except x = 2.

Answer

All negative real numbers.

Answer

All real numbers.

Answer

All positive real numbers.

Question 28

What is the inverse of the function f(x) = x² - 1?

Accepted Answer

f⁻¹(x) = ±√(x + 1)

Answer

f⁻¹(x) = x² + 1

Answer

f⁻¹(x) = 1/x² - 1

Answer

f⁻¹(x) = -x² + 1

Question 29

Which of the following transformations would shift the graph of the function f(x) = x² to the left by 3 units?

Accepted Answer

g(x) = (x + 3)²

Answer

g(x) = (x - 3)²

Answer

g(x) = x² - 3

Answer

g(x) = x² + 3

Question 30

What is the vertex of the parabola represented by the equation f(x) = 2x² - 8x + 3?

Accepted Answer

(2, -5)

Answer

(0, 3)

Answer

(-2, -1)

Answer

(1, -4)

Question 31

Which of the following is a possible graph of the inequality y > x² - 4?

Accepted Answer

A graph that is shaded above the parabola y = x² - 4.

Answer

A graph that is shaded below the parabola y = x² - 4.

Answer

A graph that is a straight line with a slope of 1.

Question 32

What is the range of the function f(x) = |x - 1| + 2?

Accepted Answer

y ≥ 2

Answer

-2 ≤ y ≤ 2

Answer

y ≤ 2

Answer

-∞ < y < ∞

Question 33

Which of the following transformations would stretch the graph of the function f(x) = sin(x) vertically by a factor of 2 without affecting its horizontal stretch?

Accepted Answer

g(x) = 2sin(x)

Answer

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

Answer

g(x) = -sin(x)

Answer

g(x) = sin(2x)

Question 34

The graph of the linear function f(x) = 2x + 1 is a straight line. What is the y-intercept of this line?

Accepted Answer

1

Answer

2

Answer

0

Answer

-1

Question 35

The graph of the quadratic function f(x) = x^2 - 4 is a parabola. What are the x-intercepts of this parabola?

Accepted Answer

x = 2 and x = -2

Answer

x = 4 and x = -4

Answer

x = 0 and x = -4

Answer

x = 1 and x = -1

Question 36

The graph of the function f(x) = |x| is a V-shaped graph. What is the effect of shifting the graph 3 units to the right?

Accepted Answer

The graph is shifted 3 units to the right. The vertex of the graph is at (-3, 0).

Answer

The graph is shifted 3 units to the left.

Answer

The graph is compressed vertically by a factor of 3.

Answer

The graph is stretched vertically by a factor of 3.

Question 37

The graph of the function f(x) = x^2 is a parabola. What is the effect of multiplying the function by -1?

Accepted Answer

The graph is reflected across the x-axis. The parabola now opens downward.

Answer

The graph is shifted 1 unit down.

Answer

The graph is stretched vertically by a factor of -1.

Question 38

The linear function f(x) = 2x + 3 has an inverse function. What is the equation of the inverse function?

Accepted Answer

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

Answer

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

Answer

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

Question 39

The graph of a function is symmetrical about the y-axis. What type of function is it?

Accepted Answer

Even function

Answer

Odd function

Answer

Linear function

Question 40

The graph of a function passes through the origin. What does this tell us about the function?

Accepted Answer

The function has a y-intercept of 0.

Answer

The function is odd.

Answer

The function is linear.

Answer

The function is quadratic.

Question 41

Which of the following functions has a vertical asymptote at x = 0?

Accepted Answer

f(x) = 1/x

Answer

f(x) = |x|

Answer

f(x) = x^2

Answer

f(x) = 2x + 1

Question 42

The graph of a function has a horizontal asymptote at y = 2. What does this tell us about the function's behavior as x approaches positive or negative infinity?

Accepted Answer

The function approaches 2 as x approaches positive or negative infinity.

Answer

The function approaches 0 as x approaches positive or negative infinity.

Answer

The function approaches infinity as x approaches positive or negative infinity.

Question 43

A patient's blood pressure is measured at different times throughout the day. The data is plotted on a graph with time on the x-axis and blood pressure on the y-axis. What type of function would best represent this data?

Accepted Answer

A function with multiple peaks and valleys

Answer

A linear function

Answer

A quadratic function

Answer

A constant function