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Manipulating the Graphs of Functions

HSF-BF.B.3
Answer Keys Here

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?