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Functions, Symmetry, and the Parent Functions
Honors Precalculus January 23 & 25, 2018 Mrs. Agnew
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Essential Question Essential Vocabulary
How do you find the domain of a function? How do you determine the symmetry of a function? Essential Vocabulary Function Parent Function Symmetry Domain Even/Odd Function
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Terminology Function: rule that assigns every x to exactly one y.
One-to-One Function? Domain: all x values for a given relation Range: all y values for a given relation Four methods of representing a function: visually, algebraically, verbally, numerically Examples: Function from graph? Domain/Range from graph
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Function Notation Useful in demonstrating how to evaluate a function for a given value of x Terminology: independent variable, dependent variable Guided Practice Page 69 #40 – 46 (Even), 70
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Symmetry with Respect to X-Axis
Test for x-axis symmetry f(x) = - f(x) If you replace y with –y, do you return the same equation? Examples… y2 = 3x – 4 |y| = 5x2 – 4 y4 = -2x + 6
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Symmetry with Respect to Y-Axis
Test for y-axis symmetry f(x) = f(-x) If you replace x with –x, do you return the same equation? Examples… x2 = 5y – 8 y = -3|x| + 7 y = x4 – 7x2 + 2
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Symmetry with Respect to Origin
Test for origin symmetry f(x) = - f(-x) If you replace y with –y AND x with -x, do you return the same equation? Examples… x4 = -3y2 + 11 x2 + y2 = 9 y = - x Examples…
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Graphing Using Symmetry
Symmetry can help us graph by using a graph’s “Mirror Image” Graphing with symmetry is really reflecting a graph over the origin, x-axis, or y-axis Examples
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Even and Odd Functions A function is EVEN if it is symmetric to the y-axis. A function is ODD if it is symmetric to the origin. What would a function be called if it were symmetric about the x-axis? Examples…
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Domain & Range Recall that the domain of a function includes all of the values of x for which the function is defined. “Problems” in Domain Denominators Square Roots Range is all of the possible values for y. Examples…
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Homework: 1/25/18 Page 69 #43, 45, 69, 85, 87, 88, 95 Worksheet Provided
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Parent Functions The parent function is the “easiest” graph of a group of functions. We will investigate parent functions for the following functions: 1. Linear Greatest Integer 2. Absolute Value 6. Reciprocal 3. Quadratic & Semicircle Square Root 8. Exponential & 4. Cubic & Logarithmic Cubic Root 9. Trigonometric
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Homework: 1/20/17 Page 69 #43, 45, 69, 85, 87, 88, 95 Worksheet Provided
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