 # Math Problems

## Question

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## Transcribed Text

Take some time, work with a classmate, think. Fill in the following table of values. No calculators. x-values y= x² f(x) = 2x² g(x) = x² - 3 h(x) = (x-3)² - -3 -2 -1 I 1 2 3 4 5 Now graph the four functions above as accurately as possible. y x² f(x) - 2x² y y 6 6 5 5 4 4 3 3 2 2 1 1 - 6 -5 -4 3. - - 2 3 4 5 6 X 1 6 -5 -4 3 - 2 - 2 3 4 5 6 X 1 2 2 3 3 -4 4 (More graph paper on next page) g(x) = x2- 3 h(x) (x-3)² - yo y g(x) = x² - 3 h(x) = (x-3)² y y 6 6 5 5 4 4 3 3 2 2 1 1 - -6 -5 -4 - 3 2 3 4 5 6 X 1 6 - -5 -4 3 2 - - 1 2 3 4 5 6 1 X 2 2 3 3 4 -4 A.) Describe the following: 1.) Which of the three functions (f(x), g(x), h(x)) makes a vertical stretch of y = x2? 2.) Which of the three functions is a horizontal shift of y = x² ? 3.) Which of the three functions is a vertical shift of y - x² ? B.) Predict. Then verify on your calculator. 1.) Find a function that looks like y x x² shifted left 2: 2.) Find a function that looks like y=x² shifted up 4, right 5: 3.) Find a function that looks like y=x² flipped upside down: 4.) Find a function that looks like y = x2 shifted vertically stretched, flipped upside down, shifted left 4 and down 2: I C.) Discuss y = a(x - h)2 + k D.) Use a TI-83 or TI-84 calculator. Tip: To put Y1 into Y2, go to VARS, click right, select 1, then select 1 again. Graph Y1 = x2- - 6x + 1 in bold Now let: A Y2 = Y1 - 3 Y3 = Y1(x-3) Y4 = -Y1 Ys = Y1(-x) (That's negative x, not "minus x") Y6 = 2Y1 Graph in pairs. Always graph Y1 and one of the other five functions. Discuss how Y2, Y3, Y4, Ys and Y6 effect the graph of Y1 E.) Change Y1 Let Y1 = Ix|. Repeat Part D, above. Let Y1 = 3 Vx Repeat Part D, above. Let Y1 = x³ - x2- - 6x Repeat Part D, above. F.) Discuss y = a f(x-h) + k for any function y = f(x). What does a control? How about h? k? s Gee.)

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