Class notes for discovering transformation of the parent graph for the square root function

FoCCM2 Lesson 4 Name ___________________________ Unit 3 – Radicals Period _______ Date _____________

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1. Parent Graph: 𝑦 = 𝑥 Answer the following questions about the parent graph 𝑦 = 𝑥 , if none exists write none. a) Domain for 𝑦 = 𝑥 is ________________________________________ b) Range for 𝑦 = 𝑥 is __________________________________________ c) y-‐intercept(s) is ____________________________________________ d) x-‐intercept(s) is ___________________________________________ TRANSFORMATIONS of 𝒚 = 𝒙

Explain by using words like left/right, up/down, reflected over, vertical stretch, and vertical shrink Using your graphing calculator sketch each graph and determine how each graph has shifted or changed shape: 2. 𝑦 = − 𝑥 a) Explain transformation of the parent graph 𝑦 = 𝑥 ___________________________________________________________ b) Domain ______________________ Range____________________ c) y-‐intercept(s) _________________ x-‐intercept(s) ______________ c) Describe the changes, if there are any, in domain, range, y-‐intercepts, and x-‐intercepts

x y -‐9 -‐4 -‐1 0 1 4 9


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3. 𝑦 = 𝑥 + 3 𝑦 = 𝑥 − 5 𝑦 = − 𝑥 + 2 a) Explain transformation of the parent graph 𝑦 = 𝑥 to 𝑦 = 𝑥 + 𝑘, how does the k effect

the graph? ______________________________________________________________________________________________________ b) Domain ______________________ Range____________________ c) y-‐intercept(s) _________________ x-‐intercept(s) ______________ c) Describe the changes, if there are any, in domain, range, y-‐intercepts, and x-‐intercepts d) What transformations were applied in the last graph? 4. 𝑦 = 𝑥 − 4 𝑦 = 𝑥 + 5 𝑦 = 𝑥 − 6+ 2 a) Explain transformation of the parent graph 𝑦 = 𝑥 to 𝑦 = 𝑥 − ℎ, how does the h effect

the graph?

______________________________________________________________________________________________________


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b) Domain ______________________ Range____________________ c) y-‐intercept(s) _________________ x-‐intercept(s) ______________

c) Describe the changes, if there are any, in domain, range, y-‐intercepts, and x-‐intercepts d) What transformations were applied in the last graph? 5. 𝑦 = 3 𝑥 𝑦 = !

!𝑥 𝑦 = −2 𝑥 − 5

a) Explain transformation of the parent graph 𝑦 = 𝑥 to 𝑦 = 𝑎 𝑥, how does the a effect

the graph? ______________________________________________________________________________________________________ b) Domain ______________________ Range____________________ c) y-‐intercept(s) _________________ x-‐intercept(s) ______________ c) Describe the changes, if there are any, in domain, range, y-‐intercepts, and x-‐intercepts d) What transformations were applied in the last graph? Summary: Given: 𝑦 = 𝑎 𝑥 − ℎ + 𝑘 Explain the change to the parent graph 𝑦 = 𝑥 for each: if 0 < 𝑎 < 1 , then vertical stretch or shrink (circle one) if 𝑎 > 0 , then vertical stretch or shrink (circle one) if 𝑥 − ℎ, then shift right or left (circle one) if 𝑥 + ℎ, then shift right or left (circle one) if 𝑥 + 𝑘, then shift up or down (circle one) if 𝑥 − 𝑘, then shift up or down (circle one)


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Lesson 5

1. What is “end behavior?” a) What Happens at the Ends? As you move farther and farther away from zero, what

does the graph look like?

• Follow the graph to very large values of x, (right-‐ positive x values)

• Follow the graph to very small values of x, (left-‐ negative x values)

2. How is the end behavior for the parabola different or the same for the square root graph? Ex.

End Behavior: End Behavior: As the value for x gets larger . . . As the value for x gets smaller . . . _____________________________________ _____________________________________ End Behavior: End Behavior: As the value for x gets larger . . . As the value for x gets smaller . . . _____________________________________ _____________________________________

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Class notes for discovering transformation of the parent graph for the square root function