Welcome! September 27, 2017 Grab your Nspire (check number) I can perform reflections across the x-axis and/or stretches away from or toward the x-axis. Grab your Nspire (check number) Book, graph paper out 3.1 Homework Questions 3.1 HW Quiz ~ Thursday 3.2 ~ Stretching and Flipping Up and Down 3.2 Practice Homework: pg. 58 3-5, handout

Warm Up: Use your Expo markers to write on your desk and complete the following. Silently!! Graphs Go Here Describe each transformation here Write the coordinate rules Write the algebraic expressions Draw a picture like the one to the right Draw in the top left box. In the top left box, draw two parabolas which open up: #1) A parabola g(x) with vertex at (0, 4) #2) A parabola h(x) with vertex at (0, -3) In the top right box, describe the transformation in words In the bottom left box, write the coordinate rules in the form: In the bottom right box, write the algebraic expressions 𝑓(𝑥)= 𝑥 2 𝑥,𝑦)→( ,

Warm Up: Partner Check Rotate two desks counter-clockwise. Check your tablemate’s work! Feel free to write comments on their work (respectfully). Have a discussion about what you think they did correctly or where they need some extra help! (Be constructive!)

Warm Up: Answer Key Graphs Go Here Describe each transformation here Write the coordinate rules Write the algebraic expressions

3.2 – Stretching and Flipping Up and Down Multiplicative Transformations of Functions If graphs of functions are related by stretching away from or toward the x-axis and/or reflecting across that axis, how are the expressions related?

Launch Video https://dashweb.pearsoncmg.co m/main.html?r=24369&p=865

Turn to page 52 in your FJ book Study the functions in the diagram. Think about how stretching or shrinking a graph vertically changes its algebraic expression. How could you write g(x) or h(x)?

Problem 3.1, pg. 52 A-D Go ahead and try it out with your tablemates! Show all work!

Problem 3.2 A (pg. 52) Complete a table of sample values for the functions f(x), g(x), and h(x) graphed on page 52. x -4 -3 2 -1 1 3 4 𝑓(𝑥)= 𝑥 2 16 9 g(x) h(x) Stop here for a discussion with group members. Think about: -Find the coordinate point (2,4) for f(x). What is the corresponding point on h(x)? What does this tell you? -Use (2,4) from f(x) again. What is the corresponding point on g(x)? What does this tell you?

Part A Answer Key

𝑓(𝑥)→𝑔(𝑥) has rule (x,y)→( , ). 𝑓(𝑥)→ℎ(𝑥) has rule (x,y)→( , ). Problem 3.2 B (pg. 53) Write rules that map the graph of 𝑓(𝑥)= 𝑥 2 onto the other graphs. 𝑓(𝑥)→𝑔(𝑥) has rule (x,y)→( , ). 𝑓(𝑥)→ℎ(𝑥) has rule (x,y)→( , ). Problem 3.2 C Based on your results of your work in A and B: What algebraic expression shows how to calculate the values for g(x)? 2. What algebraic expression shows how to calculate the values for h(x)?

Part B and C Answer Key

The graph of a piecewise-defined function s(t) is shown below. Problem 3.2 D The graph of a piecewise-defined function s(t) is shown below. On the coordinate grid, graph functions p(t), q(t), and r(t) with the properties: 1. 2. 3. 𝑝(𝑡)=3𝑠(𝑡 for all values of t q(𝑡)=0.5𝑠(𝑡 for all values of t r 𝑡 =−𝑠(𝑡 for all values of t

Part D Answer Key On the coordinate grid, graph functions p(t), q(t), and r(t) with the properties: 1. 2. 3. 𝑝(𝑡)=3𝑠(𝑡 for all values of t q(𝑡)=0.5𝑠(𝑡 for all values of t r 𝑡 =−𝑠(𝑡 for all values of t

If you finish A-D…

3.2 Homework: pg. 58 #3-5 and handout Show all work! Check answers on Weebly tonight!