Functions can be represented in a variety of forms,
such as "descriptions", "tables", "equations" and/or "graphs".

Function Description:

A function may be represented with a description of its process.

"The function will be such that each value entered
will be
multiplied times two
and added to the number one."

Function Table:

A function may be represented with a table of the ordered pairs.

A function is shown in the table at the right.
By examining the table, you can see that each y-value
is twice the corresponding x-value plus 1.

Function Equation:

A function may be represented
with an equation of the form "y =".

The equation y = 2x + 1 represents our function.
The equation may first appear in a different form
such as 2x - y = -1 or 2x - y + 1 = 0.
These are all the same equation.

Function Graph:

A function may be represented
with a graph.

The graph shows a function whose y-value is three times the x-value minus 2, or y = 3x - 2.

This graph assumes that all Real numbers can be "fed" into this function.
(All Real numbers are the domain.)

Comparing functions expressed in different forms is a popular question.

Given the two linear functions shown below:

Function 1:

x

y

0

1

1

2

2

3

3

4

Function 2:

a) Which function has the larger slope? Function 2

b) Which function has the larger y-intercept? Function 1

y-intercept has an x-value of 0. y-intercept is 1.

y-intercept is where the graph crosses the y-axis. y-intercept is -2.

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