Lesson 3.2: Connect Representations of Functions

Lesson 3.2

Connect Representations of Functions​

By Reed Carbone

Definitions:

​Linear Function: A linear function is any function where the graph of your function appears to be a line.

​

Non Linear Function: A non linear function is any function where the graph of your function is not a line. The graph could be curved, take turns, or really do anything but be a straight line.​

​

Vertical Line Test: If you can draw a vertical line on your graph and intersect your relation at at most 1 point, then your ​relation (graph) is a function. In math terms, each input (x-value) will have only 1 output (y-value).

Subject | Subject

Some text here about the topic of discussion

​Visuals:

Multiple Choice

Is this function Linear or Non-Linear?

• Linear

• Non-Linear

​Use the formula for the area of a square to create a table and graph a line. Determine whether it is a function.

Multiple Choice

Is this function Linear or Non-Linear

• Linear

• Non-Linear

​How to determine if an equation is linear or non-linear:

In an equation, if one of your variables have an exponent it is non-linear. If it does not have an exponent it is linear.

Multiple Choice

Is the function Linear or Non-Linear?

$$y^2=\ x\ +\ 5$$

• Linear

• Non-Linear

Multiple Choice

Is the function Linear or Non-Linear?

$$y\ =\ \frac{1}{2}x\ +\ 5$$

• Linear

• Non-Linear

​Determine whether each graph is a function:

Multiple Choice

Is the graph a function? Why?

• Yes, every x coordinate has more than 1 y coordinate.

• No, every x coordinate has only 1 y coordinate.

• Yes, every x coordinate has exactly 1 y coordinate.

• No, every x coordinate has more than 1 y coordinate.

Multiple Choice

Is this graph a function?

• Yes, it passes the vertical line test.

• No, it does not pass the vertical line test.

• Yes, it does not pass the vertical line test.

• No, it does pass the vertical line test.

Multiple Choice

What is the vertical line test in math terms?

• Each output will have exactly one input.

• Each input will have exactly one output.

• Every y needs an x.

• If you can draw a straight line it must work.

Multiple Choice

Is this graph a function?

• No, it does not pass the VLT

• Yes, it passes the VLT

​Conclusion: Write 2 complete sentences about what you learned.