2.7 Absolute Value Functions

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Presentation transcript:

2.7 Absolute Value Functions Learning Goals Identify the effect on the graph of replacing f(x) by f(x)+k, k*f(x),f(kx), and f(x+k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effets on the graph using technology. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

Characteristics of Absolute Value Functions shaped like a “V” symmetrical about a vertical line called the axis of symmetry domain is range is connected to the vertex, which is a minimum or maximum value

vertex : where the function reaches its maximum or minimum. To find the x-value of the vertex, set what’s inside the absolute value equal to 0.

Ex 1 Graph

Ex 2 Graph

Ex 3 Graph

Ex 4 Graph

Ex 5 Write the equation of the graph below.

Ex 5 Write the equation of the graph below.

Identify the vertex, direction of opening and if the graph is wider, narrower or the same width as the parent function.

Pg 111 #8-16 on graph paper Find vertex, domain and range Homework Pg 111 #8-16 on graph paper Find vertex, domain and range