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Honors Pre-Calc Unit 1 Day 1 --- Key Features of FunctionsName: _________________________________The following are the twelve basic parent functions. You will have to know the name and the graph behaviors for all twelve. 1. Name:_____________________________________Equation: fx=x2. Name: ____________________________________Equation: fx=x23. Name:_____________________________________Equation: fx=x3 4. Name: ___________________________________Equation fx=x5. Name: ____________________________________Equation: fx=lnx6. Name: ___________________________________Equation: fx=1x7. Name: ____________________________________Equation: fx=ex8.Name: _____________________________________Equation: fx=x9. Name: ____________________________________Equation: fx=11+ e-x10. Name: ___________________________________Equation: : fx=sin?(x)11. Name:___________________________________Equation: fx=cos?(x)110490025400012. Name: _____________________________________Equation: f(x) = [x]Extremas and Inc/Dec Intervals: Use a calculator to determine the relative (local) and absolute extrema as well as the intervals of increasing/decreasing for the following functions.Graphical Transformations: Using the twelve basic functions as a starting point we apply transformation rules to those functions to get new functions. ** Any number outside the parent function is a vertical change to the graph. Any number inside the parent function is a horizontal change to the graph. Stretches and Shrinks Horizontal stretches or shrinksVertical stretches or shrinksExample: Find the equation of the graph of fx=x2 if it undergoes the following transformations in order. A horizontal shift 2 units to the rightA vertical stretch by a factor of 3A vertical translation 5 units up Example 2: A graph of f(x) is shown. Graph g(x) = 2f(x – 1) + 1.Even/Odd/Neither:Even Functions: A symmetry of a function can be represented by an algebra statement. Reflection across the y-axis interchanges positive x-values with negative x-values, swapping x and ?x. Therefore f(?x) = f(x). The statement, “For all x ∈ R, f(?x) = f(x)” is equivalent to the statement “The graph of the function is unchanged by reflection across the y-axis.”Odd Functions: If f(x) = ?f(?x) then we have rotational symmetry about the origin. In this case, we may multiply both sides of the equation by ?1 and write f(?x) = ?f(x).2543175163830** If a graph has x-axis symmetry, it is not a function at all and thus we will not be discussing it in this unit.Example: Decide algebraically if the function is even, odd, or neither.Example 2: Decide algebraically if the function f(x) = x 5 + 7x 2 ? 3x + 5 is even, odd, or neither.Summarize: Describe the following graphs by listing the requested features.y = - |x – 2|+ 4y = 2(x – 4)3 – 5Domain: _______________________Range: ________________________Max: _________________________Min: __________________________Increasing: _____________________Decreasing: ____________________Even/Odd/Neither: ______________Translation: ____________________End Behavior: __________________Domain: _______________________Range: ________________________Max: _________________________Min: __________________________Increasing: _____________________Decreasing: ____________________Even/Odd/Neither: ______________Translation: ____________________End Behavior: __________________368617523939557150239395 Sketch:Sketch: ................
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