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Today’s Objectives: Today’s Agenda SWBAT… Sketch graphs of parent functions Define domains and ranges of common parent functions Graph functions on a calculator with a restricted domain Graph absolute value functions Name domain and range of an absolute value function 2. Notes Topic: Parent Functions Page 13 #1 – 14, 19 – 26 Handout – Absolute Value Homework:

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Constant Function f(x) = c Domain {x x } read as “x such that x belongs to the set of all real numbers.” Range {y y = c} read as “y such that y is equal to the constant value.” Features: A straight line gragh where y does not change as x changes.

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Linear Function f(x) = mx + b Domain {x x } Range {y y } Features: A straight line graph where f(x) changes at a constant rate as x changes.

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Quadratic Function f(x) = x 2 Domain {x x } Range {y y 0} Features: Graph is shape of parabola. The graph changes direction at its one vertex.

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Square Root Function f(x) = Domain {x x 0} Range {y y 0} Features: The inverse of a quadratic function where the range is restricted.

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Cubic Function f(x) = x 3 Domain {x x } Range {y y } Features: The graph crosses the x- axis up to 3 times and has up to 2 vertices

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Cube Root Function f(x) = Domain {x x } Range {y y } Features: The inverse of a cubic function

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Power Function f(x) = Domain {x x } Range {y y } Features: The graph contains the origin if b is positive. In most real- world applications, the domain is nonnegative real numbers if b is positive and positive real numbers if b is negative.

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Exponential Function f(x) = a b x Domain {x x } Range {y y > 0} Features: The graph crosses the y-axis at y = a and has the x-axis as an asymptote

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Logarithmic Function f(x) = log a x Domain {x x > 0} Range {y y } Features: The graph crosses the x- axis at 1 and has the y- axis as an asymptote.

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Absolute Value Function f(x) = Domain {x x } Range {y y 0} Features: The graph has two halves that reflect across a line of symmetry. Each half is a linear graph.

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Page 13 #1 – 14, 19 – 26 Handout – Absolute Value Homework:

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Polynomial Function http://zonalandeducation.com/mmts/func tionInstitute/polynomialFunctions/graphs /polynomialFunctionGraphs.html http://zonalandeducation.com/mmts/func tionInstitute/polynomialFunctions/graphs /polynomialFunctionGraphs.html *zero degree *first Degree *second degree *third degree Fourth degree

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