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FUNCTIONS – INTERSECTIONS, INTERPRETATIONS, AND DEEPER UNDERSTANDING

Unit Overview
In this unit, you will study graphs and function behavior including linear, quadratic, exponential, absolute value and trigonometric functions.  You will look at intersection points, intercepts, intervals where the function is positive or negative, intervals where the function increases or decreases, and end behavior. You will learn to find the midline, amplitude, and period for trigonometric graphs.  You will finish by comparing functions through word problems.

Intersection Points

Stop!  Go to Questions #1-7 about this section, then return to continue on to the next section.


Linear vs. Quadratic vs. Exponential Functions


Click on the link to watch the video "Comparing exponential and quadratic models" or click on the video.



question1Do practice here:  Compare the growth rates of exponentials and polynomials
 
Stop!  Go to Questions #8-14 about this section, then return to continue on to the next section.


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

Practice finding increasing and decreasing intervals: Increasing and decreasing intervals

Stop!  Go to Questions #18-22 about this section, then return to continue on to the next section.


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:

Click on the link to watch the video "Polynomial end behavior | Polynomial and rational functions " or click on the video.


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



question1Try 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) = 2x.


"Click here" to check the answer.

Stop!  Go to Questions #23-30 to complete this unit.