Functions: Master the Fundamentals of Functions in Math

Question 1

Which of the following equations represents a linear function?

Accepted Answer

y = 2x + 1

Answer

y = x^2 + 1

Answer

y = 2^x

Answer

y = 1/(x + 1)

Question 2

Which of the following is the vertex of the parabola f(x) = x^2 - 4x + 3?

Accepted Answer

(2, -1)

Answer

(0, 3)

Answer

(4, -13)

Answer

(3, 2)

Question 3

Solve the equation 2^x = 32.

Accepted Answer

x = 4

Answer

x = 5

Answer

x = 6

Answer

x = 3

Question 4

Which of the following graphs represents a function that is not one-to-one?

Accepted Answer

A circle with radius r centered at (0, 0)

Answer

A straight line with a positive slope

Answer

A parabola opening upward

Answer

An exponential curve

Question 5

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

Accepted Answer

All real numbers

Answer

x ≥ 1

Answer

x ≤ 1

Answer

0 ≤ x ≤ 1

Question 6

Find the equation of the exponential function that passes through the points (0, 1) and (2, 4).

Accepted Answer

f(x) = 4^x

Answer

f(x) = 2^x

Answer

f(x) = 1/2^x

Answer

f(x) = 1/4^x

Question 7

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

Accepted Answer

y = mx + b

Answer

y = x^2 + b

Answer

y = e^x + b

Answer

y = |x| + b

Question 8

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

Accepted Answer

(-∞, ∞)

Answer

[-4, ∞)

Answer

(-∞, -4]

Answer

[0, ∞)

Question 9

Which of the following functions has a decreasing range?

Accepted Answer

y = -x^2 - 1

Answer

y = x^2 + 1

Answer

y = |x| - 1

Answer

y = e^x - 1

Question 10

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 11

Which of the following is a composition of functions f(x) = x^2 and g(x) = x + 1?

Accepted Answer

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

Answer

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

Answer

f(g(x)) = x^4 + 2x^2 + 1

Answer

g(f(x)) = x^4 + x^2 + 1

Question 12

Identify the equation that represents a function:

Accepted Answer

y = x^2 + 1

Accepted Answer

y = |x|

Answer

x = y^2 + 1

Question 13

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

Accepted Answer

A function's graph is always linear

Answer

Each input has a unique output

Answer

The output values solely rely on the input values

Answer

Functions can be represented through equations, tables, or graphs

Question 14

An exponential function begins with a value of 100 and exhibits a 15% growth rate. Determine its equation.

Accepted Answer

y = 100(1.15)^x

Answer

y = 100(0.85)^x

Answer

y = 115(1.00)^x

Answer

y = 115(0.85)^x

Question 15

For the function f(x) = sqrt(x), what is its domain?

Accepted Answer

All non-negative real numbers

Answer

All real numbers

Answer

All positive real numbers

Answer

All rational numbers

Question 16

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

Accepted Answer

All real numbers

Answer

All non-negative real numbers

Answer

All positive real numbers

Answer

All odd integers

Question 17

The solution to the equation f(x) = g(x) is known as the:

Accepted Answer

Intersection point

Answer

Union

Answer

Difference

Answer

Inverse

Question 18

If a function's graph exhibits symmetry about the y-axis, what does this imply?

Accepted Answer

The graph appears identical on both sides of the y-axis

Answer

The graph is parabolic

Answer

The graph has both a maximum and minimum

Answer

The graph is linear

Question 19

Which of the following is a characteristic of a function?

Accepted Answer

Each input corresponds to exactly one output

Answer

The outputs can be repeated

Answer

The inputs depend on the outputs

Answer

The relation cannot be represented graphically

Question 20

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

Accepted Answer

[2, ∞)

Answer

(-∞, ∞)

Answer

[-2, ∞)

Answer

(-∞, 2]

Question 21

Solve the exponential equation 3^(x-1) = 27.

Accepted Answer

x = 4

Answer

x = 3

Answer

x = 5

Answer

x = 6

Question 22

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

Accepted Answer

[2, ∞)

Answer

[0, ∞)

Answer

(2, ∞)

Answer

(0, ∞)

Question 23

Which inequality represents the graph of the function f(x) = -x + 3 that is below the x-axis?

Accepted Answer

y < -x + 3

Answer

y > -x + 3

Answer

x < -y + 3

Answer

x > -y + 3

Question 24

Consider the functions f(x) = x - 1 and g(x) = x². Find (f - g)(x).

Accepted Answer

x² - 2x + 1

Answer

2x - 2

Answer

2x² - 4

Answer

x² - x + 1

Question 25

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

Accepted Answer

y = 0

Answer

y = -2

Answer

x = 0

Answer

x = -2

Question 26

Which of the following is NOT a type of function introduced in this unit?

Accepted Answer

Cubic

Answer

Linear

Answer

Quadratic

Answer

Exponential

Question 27

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

Accepted Answer

y = mx + b

Answer

y = ax^2 + bx + c

Answer

y = e^x

Answer

y = log(x)

Question 28

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 positive real numbers

Answer

All negative real numbers

Question 29

Which of the following graphs represents a quadratic function that opens upward?

Accepted Answer

U

Answer

/

Answer

\

Answer

n

Question 30

What is the range of the function g(x) = -x^2 + 4?

Accepted Answer

All real numbers greater than or equal to 0

Answer

All real numbers

Answer

All real numbers less than or equal to 4

Answer

All real numbers less than 0

Question 31

Which of the following functions is an exponential function?

Accepted Answer

y = 3^x

Answer

y = x^3

Answer

y = sin(x)

Answer

y = |x|

Question 32

What is the equation of the horizontal asymptote of the function h(x) = (x^2 + 1) / (x - 1)?

Accepted Answer

y = 1

Answer

y = 0

Answer

y = x

Answer

y = -1

Question 33

Find the y-intercept of the linear function f(x) = 2x + 5.

Accepted Answer

5

Answer

2

Answer

7

Answer

-5

Question 34

Determine the domain of the function f(x) = sqrt(x - 3).

Accepted Answer

x ≥ 3

Answer

All real numbers

Answer

x ≤ 3

Answer

x > 0

Question 35

Identify the equation of an exponential function with a base of 2.

Accepted Answer

y = 2^x

Answer

y = x^2

Answer

y = 2x

Answer

y = sqrt(x)

Question 36

Find the range of the function f(x) = -2cos(x).

Accepted Answer

[-2, 2]

Answer

[-1, 1]

Answer

[-∞, ∞]

Answer

[0, 2]

Question 37

Which of the following is the equation of a linear function with a slope 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 38

Find the vertex of the parabola y = 2x^2 + 4x - 5.

Accepted Answer

(1, -3)

Answer

(-1, -7)

Answer

(-1, -3)

Answer

(1, -7)

Question 39

Which of the following is an exponential function with a base of e?

Accepted Answer

y = e^x

Answer

y = 2^x

Answer

y = 10^x

Answer

y = ln x

Question 40

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

Accepted Answer

All real numbers greater than or equal to 1

Answer

All real numbers

Answer

All real numbers less than or equal to 1

Answer

All real numbers between 0 and 1

Question 41

Solve the inequality (x + 1)(x - 2) > 0.

Accepted Answer

x > 2 or x < -1

Answer

x < 2 or x > -1

Answer

x > -1

Answer

x < -1

Question 42

Which of the following functions is linear?

Accepted Answer

f(x) = 3x - 5

Answer

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

Answer

f(x) = 2^x

Answer

f(x) = sin(x)

Question 43

What is the slope of the line represented by the equation y = -2x + 5?

Accepted Answer

-2

Answer

2

Answer

5

Answer

-5

Question 44

What are the coordinates of the vertex of the parabola represented by the equation y = x^2 - 4x + 3?

Accepted Answer

(2, -1)

Answer

(2, 1)

Answer

(1, -1)

Answer

(1, 1)

Question 45

Which of the following functions is an exponential function?

Accepted Answer

f(x) = 2^x

Answer

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

Answer

f(x) = 3x - 5

Answer

f(x) = sin(x)

Question 46

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

Accepted Answer

[2, ∞)

Answer

(-∞, 2]

Answer

(-∞, 2)

Answer

[2, ∞]

Question 47

What is the range of the function f(x) = x^2 - 4?

Accepted Answer

[0, ∞)

Answer

(-∞, ∞)

Answer

[-4, ∞)

Answer

(-∞, -4]

Question 48

Solve the equation f(x) = 2x - 5 for x, given that f(x) = 7.

Accepted Answer

x = 6

Answer

x = 3

Answer

x = -3

Answer

x = -6

Question 49

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

Accepted Answer

f(x - 3)

Answer

f(x + 3)

Answer

f(3x)

Answer

f(x) + 3

Question 50

Which composition of functions would result in a function that is odd?

Accepted Answer

f(x) = sin(x^2)

Answer

f(x) = sin(x) + cos(x)

Answer

f(x) = sin(x) * cos(x)

Answer

f(x) = sin(x^2) + cos(x)

Question 51

Which of the following is NOT a type of function covered in this unit?

Accepted Answer

Trigonometric

Answer

Linear

Answer

Quadratic

Answer

Exponential

Question 52

What is the equation of a line 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 53

Which of the following functions has an exponential growth pattern?

Accepted Answer

f(x) = 2^x

Answer

f(x) = 2x + 1

Answer

f(x) = x^2

Answer

f(x) = log(x)

Question 54

Solve the inequality 2x - 5 > 7.

Accepted Answer

x > 1

Answer

x < 1

Answer

x < 6

Answer

x > 6

Question 55

Which of the following is 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) = -3x + 2

Question 56

Which of the following transformations will shift the graph of f(x) = x^2 left by 3 units?

Accepted Answer

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

Answer

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

Answer

f(x) = x^2 + 3

Answer

f(x) = x^2 - 3

Question 57

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

Accepted Answer

An inverted V-shaped graph with a vertex at (2, 0)

Answer

A V-shaped graph with a vertex at (2, 0)

Answer

A line with a slope of 1 and a y-intercept of 2

Answer

A line with a slope of -1 and a y-intercept of 2