Honors Alg 2 Vertical and Horizontal Translations Name______Per____
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HONORS ALG 2 VERTICAL AND HORIZONTAL TRANSLATIONS NAME______PER____
Throughout this activity, you should be using your graphing calculator to verify your thinking.
1. Graph the functions h(x) = x and j(x) = x+4 on your calculator. Describe how the function h(x) = x was “transformed” to create the graph of j(x).
2. Graph the functions f(x) = 2x and g(x) = 2x – 5 on your calculator. Describe how the function f(x) = 2x was “transformed” to create the graph of g(x).
3. For each of the 3 functions listed below, write an equation that will move the parent function “up”, an equation that will move the parent function “down”, then sketch the 3 graphs on the coordinate system provided. Function Equation to move up Equation to move down Graphs 4. Suppose you traveled at a constant speed from your house to your friends’ house 8 blocks away. Your friend met you at her house then the two of you immediately traveled back to your house at the same constant speed. The graph to the right shows how the distance from you to your friend’s house would change over time.
a. Using the parent function, determine an equation for the graph that models your trip to your friend’s house and back.
b. According to your equation, how long did the entire trip take you? Your friend?
c. Describe the changes you made in the parent function to create your equation in part a.
d. As soon as you and your friend arrived back at your house, she had to go back home. Being a good friend, you traveled home with her and then returned to your house. All the time, you traveled the same speed as you did before. Complete the graph to the right showing that you traveled back to her house then home again.
e. Using the equation you wrote for part a) above, determine an equation for the portion of the graph that models your trip to your friend’s house and back for the second time (the part you just drew).
f. Explain what changes you made in the parent function to create your equation in part d.
5. Each graph shows the parent function and a transformation of that parent function. Determine the equation of the transformed parent function. a. b. c.
d. e. f.
Check Yourself…. 1. In general, if is a positive number, how are the graphs of and related? How are the graphs of and related?
2. In general, if is a positive number, how are the graphs of and related? How are the graphs of and related?
3. Draw a careful sketch of . Identify the coordinates of the vertex, a point to the left of the vertex and a point to the right of the vertex. Then on the same coordinate axes, draw and identify the 3 points from the parent graph after the transformation. Do the same with .
4. Draw a careful sketch of . Identify the coordinates of the vertex, a point to the left of the vertex and a point to the right of the vertex. Then on the same coordinate axes, draw and identify the 3 points from the parent graph after the transformation. Do the same with .
5. Consider the following graphs:
a. Sketch c. Sketch e. Sketch b. Sketch d. Sketch f. Sketch