Functions: Master the Fundamentals of Functions in Math

Question 1

Which graph represents the function y = 2x² - 3?

Accepted Answer

A parabola opening upwards

Answer

A parabola opening downwards

Answer

A straight line with a positive slope

Answer

A straight line with a negative slope

Question 2

Solve the equation f(x) = 0 for the function f(x) = x² - 4

Accepted Answer

x = ±2

Answer

x = 2

Answer

x = -2

Answer

No solution

Question 3

Find the range of the function f(x) = 2x + 3 when the domain is {1, 2, 3}

Accepted Answer

{5, 7, 9}

Answer

{1, 2, 3}

Answer

{5, 7}

Answer

{0, 1, 2}

Question 4

Find 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 5

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

Accepted Answer

The graph is a smooth curve without any breaks.

Answer

For every input, there is at most one output.

Answer

The domain and range are both sets of numbers.

Answer

The function can be represented using an equation or a table.

Question 6

Which of the following functions has a graph that is a parabola?

Accepted Answer

y = x^2

Answer

y = x^3

Answer

y = 1/x

Answer

y = |x|

Question 7

Find the domain of the function f(x) = sqrt(x - 4).

Accepted Answer

[4, ∞)

Answer

(-∞, 4]

Answer

[0, ∞)

Answer

(-∞, ∞)

Question 8

The area of a square is given by the function A(x) = x^2. What is the perimeter of the square with an area of 25?

Accepted Answer

20

Answer

10

Answer

25

Answer

50

Question 9

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

Accepted Answer

The graph of a function is always a straight line.

Answer

Each input corresponds to exactly one output.

Answer

The output depends on the input.

Answer

The domain and range of a function are well-defined.

Question 10

Determine the slope of the graph of the function f(x) = -2x + 5.

Accepted Answer

-2

Answer

2

Answer

5

Answer

-5

Question 11

Which of the following is a translation of the function f(x) = x² by 2 units to the left?

Accepted Answer

f(x + 2)

Answer

f(2x)

Answer

f(x) + 2

Answer

f(x²) + 2

Question 12

Identify the domain of the function g(x) = √(x - 5).

Accepted Answer

x ≥ 5

Answer

x ≥ 0

Answer

x ≤ 5

Answer

All real numbers

Question 13

Which expression represents a function?

Accepted Answer

y = x^2

Answer

x + y = 5

Answer

y^2 = x

Answer

x = y^3

Question 14

Which function is linear?

Accepted Answer

f(x) = x + 3

Answer

f(x) = 2^x

Answer

f(x) = sin(x)

Answer

f(x) = 1 / x

Question 15

Calculate the slope of the line passing through (2, 5) and (4, 9).

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 16

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

Accepted Answer

All real numbers

Answer

x ≥ 1

Answer

x ≤ 1

Answer

x > 0

Question 17

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

Accepted Answer

The inputs can be repeated

Answer

Each input has exactly one output

Answer

The graph can pass the horizontal line test

Answer

The outputs can be repeated

Question 18

Which of the following equations represents a linear function?

Accepted Answer

y = 2x + 1

Answer

y = x^2

Answer

y = sin(x)

Answer

y = 1/x

Question 19

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

Accepted Answer

-2

Answer

2

Answer

5

Answer

-5

Question 20

Which of the following graphs represents a function that is decreasing and concave up?

Accepted Answer

[Image of a graph of a decreasing and concave up function]

Answer

[Image of a graph of a decreasing and concave down function]

Answer

[Image of a graph of an increasing and concave up function]

Answer

[Image of a graph of an increasing and concave down function]

Question 21

What is the equation of the line that passes through the points (2, 5) and (4, 9)?

Accepted Answer

y = x + 3

Answer

y = 2x + 1

Answer

y = ½x + 4

Answer

y = 2x - 1

Question 22

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

Accepted Answer

All real numbers

Answer

x ≥ 0

Answer

x ≤ 0

Answer

x ≥ 2

Question 23

What 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) = 2x - 1

Answer

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

Question 24

Which transformation was applied to the function f(x) = x^2 to create the function g(x) = (x - 2)² + 1?

Accepted Answer

Horizontal shift 2 units right, vertical shift 1 unit up

Answer

Horizontal shift 2 units left, vertical shift 1 unit down

Answer

Horizontal shift 1 unit right, vertical shift 2 units up

Answer

No transformation

Question 25

Which of the following statements accurately defines a function?

Accepted Answer

A mathematical relation where each input corresponds to exactly one output.

Answer

A mathematical relation where each output corresponds to at least one input.

Answer

A mathematical relation where each input corresponds to multiple outputs.

Answer

A mathematical relation where each output corresponds to multiple inputs.

Question 26

For the function f(x) = 1 / (x - 2), what is its domain?

Accepted Answer

All real numbers except 2

Answer

All real numbers except 0

Answer

All real numbers greater than 2

Answer

All real numbers

Question 27

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

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 28

Which equation below represents a quadratic function?

Accepted Answer

y = x^2 + 2x - 3

Answer

y = x^3 + 2x^2 - x + 1

Answer

y = e^x + ln(x)

Answer

y = sin(x) + cos(x)

Question 29

Which inequality is represented by the shaded region below the graph of f(x) = x^2 - 2x + 1?

Accepted Answer

y ≤ x^2 - 2x + 1

Answer

y ≥ x^2 - 2x + 1

Answer

y < x^2 - 2x + 1

Answer

y > x^2 - 2x + 1

Question 30

Determine the period of the trigonometric function f(x) = sin(2x).

Accepted Answer

2π

Answer

π

Answer

π/2

Answer

π/4

Question 31

Which of the following is the graph of the linear function f(x) = 2x + 1?

Accepted Answer

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

Answer

A parabola with a vertex at (0, 1)

Answer

A circle with a radius of 1

Answer

An ellipse with a major axis of 2

Question 32

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

Accepted Answer

x ≥ 2

Answer

x ≤ 2

Answer

x > 0

Answer

All real numbers

Question 33

Which of the following is a transformation of the function f(x) = x³?

Accepted Answer

g(x) = (x - 2)³

Answer

g(x) = -x³

Answer

g(x) = x³ + 1

Answer

g(x) = x²

Question 34

Solve the inequality f(x) > 0 for x, where f(x) = x² - 9.

Accepted Answer

x < -3 or x > 3

Answer

x > -3 and x < 3

Answer

x < -3 or x < 3

Answer

x > -3 or x < 3

Question 35

Which of the following is the inverse function of f(x) = 2x + 5?

Accepted Answer

g(x) = (x - 5) / 2

Answer

g(x) = 2x - 5

Answer

g(x) = x / 2 + 5

Answer

g(x) = 2x + 10

Question 36

Find the vertex of the function f(x) = -2x² + 8x - 3.

Accepted Answer

(2, 5)

Answer

(-2, 5)

Answer

(2, -5)

Answer

(-2, -5)

Question 37

Which transformation will shift the graph of f(x) = 2x + 3 up by 2 units?

Accepted Answer

f(x) + 2

Answer

f(x + 2)

Answer

f(x - 2)

Answer

f(x) - 2

Question 38

Find the value of x for which the function h(x) = 1/(x - 2) is discontinuous.

Accepted Answer

2

Answer

0

Answer

1

Answer

3

Question 39

Find the domain of the function: f(x) = √(x - 3)

Accepted Answer

[3, ∞)

Answer

(-∞, 3)

Answer

[0, ∞)

Answer

(-∞, ∞)

Question 40

Which of the following is the range of the function: f(x) = 2x - 1?

Accepted Answer

(-∞, ∞)

Answer

(-1, ∞)

Answer

(0, ∞)

Answer

[-1, ∞)

Question 41

Which of the following is a graph of the function: f(x) = |x|?

Accepted Answer

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

Answer

Parabola opening upwards

Answer

Horizontal line at y=0

Answer

Straight line passing through (0,0)

Question 42

Which of the following is an application of functions in real life?

Accepted Answer

Predicting weather patterns

Answer

Playing video games

Answer

Solving puzzles

Answer

Writing poems

Question 43

Identify the type of function: f(x) = sin(x)

Accepted Answer

Trigonometric function

Answer

Polynomial function

Answer

Exponential function

Answer

Rational function

Question 44

Which of the following transformations translates the graph of f(x) = x^2 up by 2 units?

Accepted Answer

f(x) = x^2 + 2

Answer

f(x) = -x^2 + 2

Answer

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

Answer

f(x) = x^2 - 2

Question 45

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

Accepted Answer

x ≥ 2

Answer

x ≤ 2

Answer

x > 2

Answer

All real numbers

Question 46

What is the range of the function *f(x) = x² + 1*?

Accepted Answer

y ≥ 1

Answer

y > 1

Answer

All real numbers

Answer

y < 1

Question 47

Which of the following equations represents a linear function?

Accepted Answer

y = 2x + 3

Answer

y = √x

Answer

y = x² - 2

Answer

y = 1/x

Question 48

The equation of a line is given as *y = -3x + 5*. What is the y-intercept?

Accepted Answer

(0, 5)

Answer

(5, 0)

Answer

(-3, 0)

Answer

(0, -3)

Question 49

Solve for *x*: 2x + 5 = 11

Accepted Answer

x = 3

Answer

x = 8

Answer

x = -8

Answer

x = -3