Functions: Definition, Types, and Applications

Question 1

Which transformation would shift the graph of y = |x| 2 units to the right?

Accepted Answer

y = |x + 2|

Answer

y = |x - 2|

Answer

y = |-x - 2|

Answer

y = |-x + 2|

Question 2

What type of function is f(x) = (x - 2)/(x + 1)?

Accepted Answer

Rational function

Answer

Polynomial function

Answer

Exponential function

Answer

Logarithmic function

Question 3

Which of the following is the domain of the periodic function f(x) = sin(x)?

Accepted Answer

(-∞, ∞)

Answer

[-1, 1]

Answer

[0, 2π]

Answer

All positive real numbers

Question 4

What is the range of the exponential function f(x) = 3^x?

Accepted Answer

(0, ∞)

Answer

(-∞, 0)

Answer

(1, ∞)

Answer

All real numbers

Question 5

How does the slope of a line relate to its rate of change?

Accepted Answer

The slope is the constant rate of change of the line.

Answer

The slope is the opposite of the rate of change.

Answer

The slope is only the rate of change when we use 'x' as the input.

Question 6

Which of the following equations represents a line with a horizontal slope (slope = 0)?

Accepted Answer

y = 0

Answer

y = 2x + 3

Answer

x = 5

Answer

y = -3

Question 7

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

Accepted Answer

x ≥ 1

Answer

x < 1

Answer

x ≥ 0

Answer

x < 0

Question 8

What is the period of the function f(x) = sin(2x)?

Accepted Answer

2π

Answer

π

Answer

π/2

Answer

4π

Question 9

Which of the following is a defining characteristic of a function?

Accepted Answer

Each input has a unique output.

Answer

The output can be any number.

Answer

The input must be a positive number.

Answer

The function can be represented as a table of values.

Question 10

Write the equation of the line with a slope of -2 and a y-intercept of 3 in slope-intercept form.

Accepted Answer

y = -2x + 3

Answer

y = 2x + 3

Answer

y = -3x + 2

Answer

y = 3x - 2

Question 11

Find the inverse of the linear function f(x) = 3x - 1.

Accepted Answer

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

Answer

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

Answer

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

Answer

f^(-1)(x) does not exist

Question 12

Which equation represents a line passing through (2, -3) with a slope of 1/2?

Accepted Answer

y = (1/2)x - 2

Answer

y = 2x - 7

Answer

y = -2x + 1

Question 13

Determine the equation of a line given its slope as 2 and y-intercept as -3.

Accepted Answer

y = 2x - 3

Answer

y = -2x + 3

Answer

y = x - 2

Answer

y = -x + 2

Question 14

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

Accepted Answer

x ≥ 2

Answer

All real numbers

Answer

x ≤ 2

Answer

x > 2

Question 15

Determine 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

Answer

f^-1(x) does not exist

Question 16

Determine the domain and range of the function: f(x) = 2x - 3.

Accepted Answer

Domain: all real numbers, Range: all real numbers

Answer

Domain: positive real numbers, Range: positive real numbers

Answer

Domain: all real numbers, Range: non-negative real numbers

Answer

Domain: non-negative real numbers, Range: all real numbers

Question 17

Identify the graph of a linear function among the following options:

Accepted Answer

A straight line

Answer

A parabola

Answer

A circle

Answer

A hyperbola

Question 18

Determine the slope of the linear function represented by the equation y = 2x + 3:

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 19

Identify the property that is not characteristic of linear functions:

Accepted Answer

Existence of a maximum or minimum value

Answer

Fixed rate of change

Answer

Representable as a straight line

Answer

Expressible as an equation in the form y = mx + b

Question 20

Find the equation of the line that passes through the points (2, 5) and (4, 11):

Accepted Answer

y = 3x - 1

Answer

y = 2x + 1

Answer

y = x + 3

Answer

y = 2x - 3

Question 21

Identify the characteristic of a function that is not one-to-one:

Accepted Answer

Multiple y-values for a single x-value

Answer

Multiple x-values for a single y-value

Answer

Must be a linear function

Answer

Fixed slope

Question 22

Determine 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 23

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

Accepted Answer

All numbers greater than or equal to 0

Answer

All real numbers

Answer

All positive real numbers

Answer

All negative real numbers

Question 24

Identify a practical application of linear functions in the real world:

Accepted Answer

Calculating the total cost of a purchase

Answer

Predicting the weather for the next day

Answer

Finding the volume of a sphere

Answer

Solving a quadratic equation

Question 25

Which property is NOT true for a function?

Accepted Answer

Inputs can be repeated.

Answer

Each input has only one output.

Answer

Functions can be written as equations.

Answer

The output of a function is determined by its input.

Question 26

Which of the following equations represents a line with 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 27

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

Accepted Answer

All real numbers except for 2

Answer

All real numbers

Answer

All positive real numbers

Answer

All negative real numbers

Question 28

Which of the following equations represents the line perpendicular to the line y = 2x - 1 and passing through the point (3, 5)?

Accepted Answer

y = -(1/2)x + 8

Answer

y = (1/2)x + 8

Answer

y = -(1/2)x + 4

Answer

y = (1/2)x + 4

Question 29

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

Accepted Answer

All non-negative real numbers

Answer

All positive real numbers

Answer

All real numbers

Answer

All non-positive real numbers

Question 30

Which of the following is NOT a transformation that can be applied to the graph of a function?

Accepted Answer

Changing the range

Answer

Vertical translation

Answer

Horizontal translation

Answer

Reflection over the x-axis

Question 31

Which of the following is a characteristic of a function?

Accepted Answer

Each input has a unique output

Answer

The domain consists of all possible output values

Answer

The range consists of chosen input values

Answer

The same output can correspond to multiple inputs

Question 32

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

Accepted Answer

x ≥ 2

Answer

x ≤ 2

Answer

All real numbers

Answer

x > 0

Question 33

Which of the following graphs represents a linear function?

Accepted Answer

A straight line

Answer

A parabola

Answer

A circle

Question 34

Which of the following is a defining characteristic of a linear function?

Accepted Answer

Constant rate of change

Answer

Curved graph

Answer

Constant second derivative

Question 35

The graph of a quadratic function is a:

Accepted Answer

Parabola

Answer

Line

Answer

Hyperbola

Answer

Circle

Question 36

Which of the following is the equation of the line with slope = 3 and y-intercept = -2?

Accepted Answer

y = 3x - 2

Answer

y = -3x - 2

Answer

y = -3x + 2

Answer

y = 3x + 2

Question 37

The graph of the function f(x) = |x| is considered:

Accepted Answer

V-shaped

Answer

Linear

Answer

Circular

Answer

Parabolic

Question 38

The function f(x) = 2x + 1 can be classified as a:

Accepted Answer

Linear function

Answer

Quadratic function

Answer

Logarithmic function

Answer

Exponential function

Question 39

Which of the following functions represents an inverse variation?

Accepted Answer

f(x) = k/x

Answer

f(x) = kx

Answer

f(x) = k^x

Answer

f(x) = x^k

Question 40

Which of the following sets of ordered pairs represents a function?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 41

What is the slope of the line that passes through the points (2, 5) and (4, 1)?

Accepted Answer

-2

Answer

-1/2

Answer

1/2

Answer

2

Question 42

Which equation represents a line with a slope of 3 and a y-intercept of -1?

Accepted Answer

y = 3x - 1

Answer

y = -3x + 1

Answer

y = 3x + 1

Answer

y = -1x + 3

Question 43

The graph of a linear function is always a _________.

Accepted Answer

straight line

Answer

hyperbola

Answer

circle

Answer

parabola

Question 44

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 except 0

Question 45

Given the function f(x) = 2x + 1, what is the value of f(3)?

Accepted Answer

7

Answer

5

Answer

3

Answer

9

Question 46

The equation y = -2x + 5 represents a line with a slope of ______ and a y-intercept of ______.

Accepted Answer

-2, 5

Answer

-5, 2

Answer

2, -5

Answer

5, -2

Question 47

Which equation represents a horizontal line?

Accepted Answer

y = 4

Answer

x = 4

Answer

y = 4x

Answer

x = 4y

Question 48

A function whose graph is a straight line is called a ______ function.

Accepted Answer

linear

Answer

exponential

Answer

quadratic

Answer

logarithmic

Question 49

If a linear function has a slope of 0, what does its graph look like?

Accepted Answer

A horizontal line

Answer

A curve

Answer

A diagonal line

Answer

A vertical line