Name ___________________________________________ Date ______________________ Hour ______________

E-2: Types of Functions

First, recall… what makes a relation a function?

Circle all of the following that are functions:

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Today we are assuming every relation we’re given is a function. There are 3 types of functions we will focus on in

Algebra 1. Those are _______________, ______________________, and _____________________. It is important to be

able to identify what type of function you are dealing with based on a table, a graph, or an equation.

With tables, check the first and second differences for the y values.

Table A: Table B: Table C:

In Table A, the _______________________________ is the same so it is a ___________________ function.

In Table B, the ________________________________ is the same so it is a ______________________ function.

In Table C, the ___________________________________________ is the same so it is an _________________ function.

x y

-2 -1

-1 1

0 3

1 5

2 7

x y

-2 6

-1 3

0 2

1 3

2 6

x y

-2 1

4

-1 1

2

0 1

1 2

2 4

With graphs, you are looking at the shape of the function.

A linear graph is simply a straight line… while a quadratic has a U shape… and exponential is a sort of ramp shape.

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The last way a function to identify could be given to you is in the form of an equation.

Linear equations have an x with an exponent of 1. They are in the form: _______________________ (remember that you

can also have special linear equations- horizontal in the form ____________ and vertical in the form _____________).

Quadratic equations have an x with the largest exponent being 2. They are in the form: ___________________________.

The 2 part of the equation is what makes the equation into a quadratic equation.

Exponential equations have an x as the exponent and a number as a base. They are in the form: __________________.

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We can not only describe the type of function, but also the properties of the function.

Linear functions are either _______________________ or ___________________________.

Increasing linear: or a positive slope in an equation or y-values increasing in a table

Decreasing linear: or a negative slope in an equation or y-values decreasing in a table

Quadratic functions are either _____________________________ or ___________________________.

Positive quadratic: or a positive x2 in an equation or a positive 2nd difference in a table

Negative quadratic: or a negative x2 in an equation or a negative 2nd difference in a table

Exponential functions are called either _________________________ or ___________________________.

Exponential growth: or a b-value greater than 1 in an equation or multiplying a ratio to the

2nd differences in a table

Exponential decay: or a b-value between 0 and 1 in an equation or dividing a ratio to the 2nd

differences in a table

Let’s look at how these functions “grow”. Use your calculator to evaluate each function (substitute in the “x” value in the

left column) and see which one gets bigger, faster. The first two rows have been done for you.

y = x y = x2

y = 2x

1 y = 2(1) = 2 y = 2(1)2 = 2(1) = 2 y = 21 = 2

2 y = 2(2) = 4 y = 2(2)2 = 2(4) = 8 y = 22 = 4

3 y = 2(___) = ____ y = 2(__)2 = 2(___) = ___ y = 2___ = ___

4 y = 2(___) = ____ y = 2(__)2 = 2(___) = ___ y = 2___ = ___

5 y = 2(___) = ____ y = 2(__)2 = 2(___) = ___ y = 2___ = ___

6 y = 2(___) = ____ y = 2(__)2 = 2(___) = ___ y = 2___ = ___

7 y = 2(___) = ____ y = 2(__)2 = 2(___) = ___ y = 2___ = ___

8 y = 2(___) = ____ y = 2(__)2 = 2(___) = ___ y = 2___ = ___

9 y = 2(___) = ____ y = 2(__)2 = 2(___) = ___ y = 2___ = ___

10 y = 2(___) = ____ y = 2(__)2 = 2(___) = ___ y = 2___ = ___

As the x-values you put in get larger, over time, one type of equation grows the fastest: _______________________.

We will do some problems from the homework as a class for the examples. The rest of the homework is yours to do

individually. The problems we will do together are: 7, 8, 11, 12, 14, and 22.