FUNCTIONS – INTERSECTIONS, INTERPRETATIONS, AND DEEPER UNDERSTANDING

Linear vs. Quadratic vs. Exponential Functions

Function Features

In this section, you will identify key features of a function including intercepts, intervals where the function is increasing or decreasing, intervals where it is positive or negative, maximums and minimums, and end behavior. You will also look at features of trigonometric functions including amplitude, midline, and periodicity.

Finding x-intercepts and y-intercepts



Stop!  Go to Questions #15-17 about this section, then return to continue on to the next section.

Increasing/Decreasing and Positive/Negative Intervals

Watch this video that explains when a function is increasing or decreasing as well as intervals where the function is positive and where the function is negative.

Click on the link to watch the video "Introduction to increasing, decreasing, positive or negative intervals " or click on the video.

Click on the link to watch the video "Positive and negative intervals examples | Functions and their graphs " or click on the video.

Practice finding positive and negative intervals:   Positive and negative intervals

Stop!  Go to Questions #18-26 about this section, then return to continue on to the next section.

Trigonometric Functions

Try this! Find the midline, amplitude, and period of the following graph.

The reflected point is (1, 0).

Click here to check your answer for midline.

Click here to check your answer for amplitude.

Click here to check your answer for period.

End Behavior

End behavior is how we describe what a graph does at the "ends" or how it continues on in both directions. We describe what a graph does as x continues to positive infinity and what the graph does as x continues to negative infinity.

Watch these videos to see examples of end behavior.

Video 1:

Video 2:
Click on the link to watch the video "Recognizing features of functions" or click on the video.

Try this!  Look at the graph below and state the end behavior as x becomes more positive and as x becomes more negative.  As review, also state the y-intercept by looking at the graph as well as the interval where the function is positive. 
This is an exponential function, f (x) = 2^x.

Stop!  Go to Questions #37-41 about this section, then return to continue on to the next section.

Word Problems

Click on the link to watch the video "Applying the quadratic formula | Quadratic equations" or click on the video.

Video 1:

Click on the link to watch the video "Modeling with combined functions | Functions and their graphs " or click on the video.

Video 2:

Click on the link to watch the video "Comparing linear functions word problems 2" or click on the video.

Video 3:

Click on the link to watch the video "Comparing linear functions word problems 3" or click on the video.

Practice:

Model situations by combining functions using arithmetic operations

Constructing linear functions word problems

Stop!  Go to Questions #42-47 to complete this unit.