Functions: Definition, Types, and Properties - Mathematics for Business

Question 1

Which property is characteristic of a linear function?

Accepted Answer

Constant slope

Answer

Curved graph

Answer

Symmetrical about the y-axis

Answer

Assymptotic behavior

Question 2

In business, which function type is often used to model revenue over time?

Accepted Answer

Exponential

Answer

Linear

Answer

Quadratic

Answer

Logarithmic

Question 3

What is 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 + 1

Answer

f^-1(x) does not exist

Question 4

A function that is both one-to-one and onto is known as a:

Accepted Answer

Bijection

Answer

Surjection

Answer

Injection

Answer

Permutation

Question 5

Which of the following functions is increasing?

Accepted Answer

f(x) = x^3

Answer

f(x) = -2x^2

Answer

f(x) = 1/x

Answer

f(x) = -e^x

Question 6

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

Accepted Answer

[0, ∞)

Answer

[2, ∞)

Answer

(-∞, ∞)

Answer

[0, 2]

Question 7

Which property is NOT characteristic of functions?

Accepted Answer

Symmetry

Answer

Domain

Answer

Range

Answer

Injectivity

Question 8

In the linear function equation y = mx + c, 'm' represents:

Accepted Answer

The slope

Answer

The y-intercept

Answer

The x-intercept

Answer

The range

Question 9

The graph of a quadratic function forms a:

Accepted Answer

Parabola

Answer

Straight line

Answer

Circle

Answer

Hyperbola

Question 10

An exponential function with a positive base and exponent greater than 1 is:

Accepted Answer

Increasing

Answer

Decreasing

Answer

Constant

Answer

Periodic

Question 11

The inverse of the function f(x) = x^2 + 1 is:

Accepted Answer

f^-1(x) = ±√(x-1)

Answer

f^-1(x) = -√(x-1)

Answer

f^-1(x) = √(x-1)

Answer

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

Question 12

The range of the function f(x) = -x^2 + 4 is:

Accepted Answer

All real numbers greater than or equal to -4

Answer

All real numbers less than or equal to 4

Answer

All real numbers greater than or equal to 4

Answer

All real numbers less than or equal to -4

Question 13

A function that has an inverse function is known as a:

Accepted Answer

Bijective function

Answer

Increasing function

Answer

Decreasing function

Answer

Constant function

Question 14

Which of the following is the standard notation for expressing a function?

Accepted Answer

f(x)

Answer

x(f)

Answer

xf

Answer

fx

Question 15

Identify the type of function represented by the equation y = 3x - 2:

Accepted Answer

Linear

Answer

Cubic

Answer

Exponential

Answer

Quadratic

Question 16

Determine the domain of the function f(x) = 1 / (x + 3):

Accepted Answer

All real numbers except -3

Answer

All negative real numbers

Answer

All positive real numbers

Answer

All real numbers

Question 17

Find the inverse function of f(x) = 2x + 5:

Accepted Answer

f^-1(x) = (x - 5) / 2

Answer

f^-1(x) = 1 / (2x + 5)

Answer

f^-1(x) = 2x - 5

Answer

f^-1(x) = x / 2 - 5

Question 18

Determine the range of the function f(x) = -|x|:

Accepted Answer

All non-positive real numbers

Answer

All negative real numbers

Answer

All positive real numbers

Answer

All real numbers

Question 19

Identify the graph that represents a quadratic function with a negative leading coefficient:

Accepted Answer

A parabola opening downwards

Answer

A straight line

Answer

A parabola opening upwards

Question 20

Which of the following functions is an exponential function?

Accepted Answer

f(x) = 3^(2x)

Answer

f(x) = 2x

Answer

f(x) = x^3

Question 21

Which of the following represents a linear function?

Accepted Answer

y = 2x + 5

Answer

y = e^x

Answer

y = x³ - 1

Answer

y = sin(x)

Question 22

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

Accepted Answer

All real numbers except x = 2

Answer

x > 2

Answer

x ≠ 0

Answer

x < 2

Question 23

Determine the gradient of the graph of the function f(x) = 3x - 2.

Accepted Answer

3

Answer

2

Answer

-3

Answer

-2

Question 24

Which of the following represents the composition of the functions f(x) = x² and g(x) = x + 1?

Accepted Answer

f(g(x))

Answer

g(f(x)) - f(g(x))

Answer

g(f(x))

Answer

f(g(x)) + g(f(x))