## Manipulating the Graphs of Functions

#### Aligned To Common Core Standard:

**High School Building Functions** - HSF-BF.B.3

Is There a Pattern to the Graphs of Functions? A pattern is anything that repeats itself, i.e., a particular action taking place again and again at regular intervals. In this way, a straight line is a pattern where all the points that are connected with each other are formed on the same plane. Suppose you have an equation to graph x + y = 7. The equation means that when the two variables are added, you get 7. They can 1 and 6, 5 and 2, 4 and 3 or 7 and 0. Given that we put these numbers in the form of a table and start plotting them accordingly, we will get a pattern that will be represented in the form of a straight line. When placed on a graph, the pattern is evident as when we join all the points, it forms a straight line. This series of worksheets and lessons has students learn to work their way around with graphs of functions. The purpose being to use them to your advantage.

### Printable Worksheets And Lessons

- Graph Changes Step-by-step
Lesson- If you change the value of the y-intercept, how does
it change the graph of the function?

- Guided Lesson
- It is really neat to work this through with kids on a graphing
calculator, so they can instantly see the difference.

- Guided Lesson Explanation
- I use to have kids make moving line flip books to illustrate this.
It's a fun activity!

- Practice Worksheet
- A true mix of changes that students must evaluate at every corner.

- Matching Worksheet
- Looking back, I did truly over explain some of these.

#### Homework Sheets

There are a great number of variables to digest here with these problems.

- Homework 1 - Using the function y = 2x + 5, which statement best describes the effect of increasing the y-intercept by 5?
- Homework 2 - Both lines are parallel, so the slope is the same. No, the lines does not touch the origin (0,0).
- Homework 3 - Rewrite the equation with the double of slope and leave the y intercept the same.

#### Practice Worksheets

Understanding the value and trends of the slope of the line are truly key here.

- Practice 1 - Which is it? : a. The new line is parallel to the original. b. The new line has greater rate of change.
- Practice 2 - Which best represents this line if the slope is doubled and the y-intercept remains constant?
- Practice 3 - Step by step answers for you.

#### Math Skill Quizzes

When do these lines pass through the origin?

- Quiz 1 - The graph of a line that contains the points (-1, -6) and (4, 9) is shown below.
- Quiz 2 - Which statement best describes the effect on the graph of f(x) = 6x - 2. If the y intercept is changed to + 1?
- Quiz 3 - Using the function y = 6x + 2, which statement best describes the effect of increasing the yintercept by 3?