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Transformations of Functions
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Warm-Up # How is G(x) translated from f(x)? G(x) = f(x) + 4 G(x) = f(x) – 5 G(x) = f(x – 6 ) G(x) = f(x + 7) Make sure you have a calculator at the beginning of the period for each day from now on!!
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HW Check – Transformations WS.
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Essential Question ( ) 2. How can we model transforming Quadratic functions with an equation?
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Recall: What is a Function?
A FUNCTION is a relation that maps each x-value (domain) to EXACTLY one y-value (range). ***Meaning X values CANNOT Repeat*** Remember The domain = your x-values or input The Range = your y-values or output
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Characteristics points at
What does the graph of look like? U Shaped Lowest point is at the origin (0,0) Opens up Symmetrical Called a “Parabola” Characteristics points at (-2, 4), (-1, 1), (0,0), (1,1), (2, 4)
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**Outside of Parenthesis** - Not with the “x”
+ Moves up – Moves down
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**Inside the Parenthesis** - With the “x”
+ Moves LEFT – Moves right
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Multiply by a “-” (negative)
Reflects across the x-axis
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Multiply by a # If # > 1 then it makes the quadratic more narrow “Vertical Stretch” – Pulling up towards the y-axis If 0 < # < 1 then is makes the quadratic wider “Vertical Compression” – pulling away from the y-axis
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Warm-up 1 Solve the following quadratics Using the discriminat, determine the number and type of solutions for the quadratic: 3.
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