Functions are like mathematical machines that perform operations on an input in order to produce an output. Knowing what type of function you are dealing with is just as important as working the problem itself. The equations below are grouped according to their function. For each equation, four possible functions are listed, with the correct answer in bold. To present these equations as a quiz or exam, simply copy them onto a word-processing document and remove the explanations and boldface type. Or, use them as a guide to help students review functions.

## Linear Functions

A linear function is any function that graphs to a straight line, notes Study.com:

"What this means mathematically is that the function has either one or two variables with no exponents or powers."

*y - 12x = 5x + 8*

A) Linear

B) Quadratic

C) Trigonometric

D) Not a Function

*y = 5*

A) Absolute ValueB) Linear

C) Trigonometric

D) Not a Function

## Absolute Value

Absolute value refers to how far a number is from zero, so it is always positive, regardless of direction.

*y* = |*x* - 7|

A) Linear

B) TrigonometricC) Absolute Value

D) Not a Function

## Exponential Decay

Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time and can be expressed by the formula *y=a(1-b) ^{x }*where

*y*is the final amount,

*a*is the original amount,

*b*is the decay factor, and

*x*is the amount of time that has passed.

*y* = .25^{x }

A) Exponential GrowthB) Exponential Decay

C) Linear

D) Not a Function

## Trigonometric

Trigonometric functions usually include terms that describe the measurement of angles and triangles, such as sine, cosine, and tangent, which are generally abbreviated as sin, cos, and tan, respectively.

*y* = 15*sinx*

A) Exponential GrowthB) Trigonometric

C) Exponential Decay

D) Not a Function

*y* = *tanx*

A) Trigonometric

B) Linear

C) Absolute Value

D) Not a Function

## Quadratic

Quadratic functions are algebraic equations that take the form: *y* = *ax*^{2 }+ *bx* + *c*, where *a* is not equal to zero. Quadratic equations are used to solve complex math equations that attempt to evaluate missing factors by plotting them on a u-shaped figure called a parabola, which is a visual representation of a quadratic formula.

*y* = -4*x*^{2} + 8*x* + 5

A) Quadratic

B) Exponential Growth

C) Linear

D) Not a Function

*y* = (*x* + 3)2

A) Exponential GrowthB) Quadratic

C) Absolute Value

D) Not a Function

Exponential growth is the change that occurs when an original amount is increased by a consistent rate over a period of time. Some examples include the values of home prices or investments as well as the increased membership of a popular social networking site.

*y* = 7^{x }

A) Exponential Growth

B) Exponential decay

C) Linear

D) Not a function

## Not a Function

In order for an equation to be a function, one value for the input must go to only one value for the output. In other words, for every *x*, you would have a unique *y*. The equation below is not a function because if you isolate *x *on the left side of the equation, there are two possible values for *y*, a positive value and a negative value.

x^{2 }+ y^{2} = 25

A) Quadratic

B) Linear

C) Exponential growthD) Not a function