Functions: Definition, Types, and Applications

Question 1

Which of the following is the inverse function of 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 2

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

Accepted Answer

y ≥ 3

Answer

y ≤ 3

Answer

y < 3

Answer

y > 3

Question 3

Which of the following is the equation of the line of symmetry for the graph of the function f(x) = x^2?

Accepted Answer

x = 0

Answer

y = x

Answer

y = -x

Answer

y = 0

Question 4

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

Accepted Answer

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

Answer

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

Answer

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

Answer

f^-1(x) does not exist

Question 5

Identify the graph that represents the function f(x) = (x - 2)^2 + 1.

Accepted Answer

Parabola with vertex at (2, 1)

Answer

Parabola with vertex at (0, 1)

Answer

Parabola with vertex at (2, 0)

Answer

Straight line with slope 1 and y-intercept 1

Question 6

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

Accepted Answer

y ≥ 1

Answer

y > 1

Answer

y < 1

Answer

y ≤ 1

Question 7

Find the equation of the line of symmetry for the function f(x) = x^2 - 4.

Accepted Answer

x = 0

Answer

x = 2

Answer

x = -2

Answer

x = 4

Question 8

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

Accepted Answer

The graph of a function is always a straight line

Answer

Each input has exactly one output

Answer

The output values are dependent on the input values

Answer

The domain and range can be any sets of numbers

Question 9

Determine the domain of the function f(x) = √(x + 2).

Accepted Answer

x ≥ -2

Answer

x ≤ -2

Answer

All real numbers

Answer

The empty set

Question 10

Which of the following represents the equation of the inverse function of f(x) = 2x - 3?

Accepted Answer

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

Answer

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

Answer

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

Answer

f^-1(x) does not exist

Question 11

Which of the following is the correct representation for the function f(x) = x^2 + 4x + 3?

Accepted Answer

A parabola that opens upwards

Answer

A straight line with a positive slope

Answer

A graph that is symmetric about the x-axis

Answer

A hyperbola

Question 12

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

Accepted Answer

All numbers except 2

Answer

x > 2

Answer

x < 2

Answer

All real numbers

Question 13

Which of the following represents 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

Answer

f^-1(x) does not exist

Question 14

What is the equation of the line of symmetry for the graph of f(x) = x^2 - 4x + 3?

Accepted Answer

x = 2

Answer

x = -2

Answer

y = 2

Answer

y = 3

Question 15

Which expression represents the composite function f(g(x))?

Accepted Answer

(f ∘ g)(x) = f(g(x))

Answer

(f ∘ g)(x) = f(x) + g(x)

Answer

(g ∘ f)(x) = f(g(x))

Answer

(g ∘ f)(x) = f(x) + g(x)

Question 16

Determine the domain of the function y = 1/(x-2).

Accepted Answer

All real numbers except 2

Answer

All real numbers

Answer

All real numbers greater than 2

Answer

All real numbers less than 2

Question 17

Identify the range of the function y = x^2.

Accepted Answer

All non-negative real numbers

Answer

All real numbers

Answer

All positive real numbers

Answer

All negative real numbers

Question 18

Identify the range of the function y = |x|.

Accepted Answer

All non-negative real numbers

Answer

All real numbers

Answer

All positive real numbers

Answer

All negative real numbers

Question 19

Describe the graph of the function y = 2^(x-1).

Accepted Answer

An exponential curve increasing from left to right

Answer

A parabola opening upwards

Answer

A parabola opening downwards

Answer

An exponential curve decreasing from left to right

Question 20

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

Accepted Answer

All real numbers except x = 2

Answer

All real numbers

Answer

x > 2

Answer

x < 2

Question 21

Which of the following functions is even?

Accepted Answer

f(x) = |x|

Answer

f(x) = x^3

Answer

f(x) = sin(x)

Answer

f(x) = e^x

Question 22

Which of the following is the graph of the function f(x) = 1/x?

Accepted Answer

Hyperbola with asymptotes y = 0 and x = 0

Answer

Horizontal line at y = 1

Answer

Vertical line at x = 1

Answer

Parabola with vertex (0, 1)

Question 23

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

Accepted Answer

The output can correspond to multiple inputs

Answer

The input and output are related

Answer

The output is unique

Answer

The input is unique

Question 24

Find the range of the function f(x) = 2x + 1.

Accepted Answer

All real numbers

Answer

x > 1

Answer

x ≤ 1

Answer

x ≥ 1

Question 25

Which of the following is a composite function?

Accepted Answer

f(g(x))

Answer

f(x) + g(x)

Answer

f(x) - g(x)

Answer

f(x) * g(x)

Question 26

Which expression represents a quadratic function?

Accepted Answer

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

Answer

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

Answer

f(x) = |x| + 1

Answer

f(x) = √x + 2

Question 27

Find the vertex of the parabola f(x) = (x - 2)^2 + 1.

Accepted Answer

(2, 1)

Answer

(2, 0)

Answer

(0, 1)

Question 28

Which characteristic is NOT applicable to functions?

Accepted Answer

A single input can produce multiple outputs

Answer

The input set defines the domain

Answer

The output set defines the range

Question 29

Which of the following represents a composite function?

Accepted Answer

f(g(x))

Answer

f(x) * g(x)

Answer

f(x) - g(x)

Answer

f(x) + g(x)

Question 30

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 31

Identify the type of graph that represents the function f(x) = -x + 2.

Accepted Answer

A line with a negative slope and a y-intercept of 2

Answer

A line with a positive slope and a y-intercept of 2

Answer

A parabola opening upwards with a vertex at (0, 2)

Question 32

Identify the linear function from the following options.

Accepted Answer

f(x) = 2x - 1

Answer

f(x) = 1 / x

Answer

f(x) = sin(x)

Answer

f(x) = x^2 + 3

Question 33

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

Accepted Answer

x = 2

Answer

x = -1

Answer

x = 1

Answer

x = 0

Question 34

Determine the range of the function f(x) = x^2 + 2.

Accepted Answer

[2, ∞)

Answer

(-2, ∞)

Answer

[-2, ∞]

Answer

(0, ∞)

Question 35

Is the function f(x) = 2x + 3 one-to-one?

Accepted Answer

Yes

Answer

Cannot be determined

Answer

None of the above

Answer

No

Question 36

Which of the following is the graph of the function f(x) = |x| + 1?

Accepted Answer

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

Answer

Straight line with slope 1

Answer

Parabolic graph opening upwards

Answer

Circular graph

Question 37

What are the zeros of the function f(x) = x^3 - 8?

Accepted Answer

x = 2, ±2i

Answer

x = 4, ±2i

Answer

x = 2, ±8i

Answer

x = 2, ±4i

Question 38

What is the composite function f(g(x)) given f(x) = sqrt(x) and g(x) = x + 1?

Accepted Answer

f(g(x)) = sqrt(x + 1)

Answer

f(g(x)) = x + sqrt(1)

Answer

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

Answer

f(g(x)) = 1 - sqrt(x)

Question 39

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

Accepted Answer

x ≥ 2

Answer

All real numbers

Answer

x < 2

Question 40

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

Accepted Answer

7

Answer

6

Answer

5

Question 41

Which of the following graphs represents a function?

Accepted Answer

A graph that passes the vertical line test

Answer

A parabola

Answer

A graph that passes the horizontal line test

Answer

A circle

Question 42

What is the range of the function h(x) = x² - 4?

Accepted Answer

y ≥ -4

Answer

All real numbers

Answer

y > -4

Answer

y ≤ -4

Question 43

Which of the following is NOT a valid way to represent a function?

Accepted Answer

A table with repeating x-values

Answer

An equation

Answer

A set of ordered pairs

Answer

A graph

Question 44

A function is defined by the rule: 'Multiply the input by 2 and then subtract 5'. What is the function's algebraic representation?

Accepted Answer

f(x) = 2x - 5

Answer

f(x) = x² - 5

Answer

f(x) = 2(x - 5)

Answer

f(x) = 5 - 2x

Question 45

The graph of a function is a straight line passing through the points (0, 2) and (1, 5). What is the function's equation?

Accepted Answer

f(x) = 3x + 2

Answer

f(x) = -3x + 2

Answer

f(x) = 3x - 2

Answer

f(x) = 2x + 3

Question 46

If f(x) = x² and g(x) = x - 1, what is the resulting function (f o g)(x)?

Accepted Answer

(x - 1)²

Answer

x² - 1

Answer

x² - x

Answer

x² + x - 1