Graphs of Functions

4 3 2 1 0In addition to level 3.0 and beyond what was taught in class, the student may: Make

connection with other concepts in math.

Make connection with other content areas.

 

The student will understand and explain the difference between functions and non-functions using graphs, equations, and tables. Compare

properties of a function to a non-function.

The student will be able to model and evaluate functions and non-functions. Use graphs,

equations, and tables to determine functions and non-functions.

 

With help from theteacher, the student has partial success with level 2 and 3 elements.

Even with help, students have no success with the functions.

Focus 6 - Learning Goal #1: Students will understand and explain the difference between functions and non-functions using graphs, equations, and tables.

A function is a rule that relates two quantities so that each input value corresponds to exactly one output value.

Define-

In order for a graph to be a function, each x can only have ONE y.

Give an example of why this graph is not a function.

Is this graph a function? Why or why not?

Yes, each x input has only one y output.

Is this graph a function? Why or why not?

NO, each x input has more than one y output.

Is this graph a function? Why or why not?

Yes, each x input has only one y output.

Vertical Line Test

When looking at a graph, you can tell if a drawing is a function if it passes the vertical line test.

This means you can draw a vertical line and it will only touch the drawing (graphed figure) one time.

If it touches the drawing (graphed figure)

more than once, it is not a function.

Determine if the relationship represents a function. Does it pass the vertical line test?

The relationship is not a function.

Determine if the relationship represents a function. Does it pass the vertical line test?

The relationship is a function.

x

y

Determine if the relationship represents a function. Does it pass the vertical line test?

The relationship is a function.

Parts of a graph… Increase – A function is

“increasing” when the y-value increases as the x-value increases.

Interval – A section of the graph. ◦ This function is increasing for the

interval shown. It may be increasing or decreasing elsewhere.

Decrease – A function is “decreasing” when the y-value decreases as the x-value increases.

Parts of a graph…

Linear: A function is linear when it makes a straight line.

*Each part of this graph is linear because each section is a straight line.

Non-Linear: A function is non-linear when it is curved.

*Each part of this graph is non-linear because each section is curved.

At what intervals is this function increasing?

Intervals are written in between brackets [ ].

1. [0.5, 1] This means it is increasing from 0.5 to 1 along the x-axis.

2. [2, 3]This means it is increasing from 2 to 3 along the x-axis.

At what intervals is this function decreasing?

1. [-1, 0.5] This means it is decreasing from -1 to 0.5 along the x-axis.

2. [1, 2]This means it is decreasing from 1 to 2 along the x-axis.

At what intervals is this function linear?

1. [-1, 0] This means it is linear from -1 to 0 along the x-axis.

2. [1, 2]This means it is linear from 1 to 2 along the x-axis.

At what intervals is this function non-linear?

1. [0, 1] This means it is non-linear from 0 to 1 along the x-axis.

2. [2, 3]This means it is decreasing from 2 to 3 along the x-axis.