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Graphing and Writing Absolute Value Functions

Learn how to graph and write absolute value functions and apply transformations. Identify intercepts, zeros, intervals of increase and decrease. Compare graphs and apply symmetry.

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Graphing and Writing Absolute Value Functions

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  1. Friday, September 3 Essential Questions • How do I graph and write absolute value functions?

  2. 2.4 Use Absolute Value Functions and Transformations Graph a function of the form . Example 1 Graph . Identify the intercepts, zeros, and intervals of increase and decrease. Compare the graph with the graph . • Identify and plot the vertex, • Plot another point on the graph such as Use symmetry to plot a third point, • Connect the points with a ____________ graph. V-shaped • Examine the graph. The x-intercepts are ____ and ____, which are also the _______ of the function, and the y-intercept is ____. The function is increasing when _________ and decreasing when ________. zeros

  3. 2.4 Use Absolute Value Functions and Transformations Graph a function of the form . Example 1 Graph . Identify the intercepts, zeros, and intervals of increase and decrease. Compare the graph with the graph . • Compare with . The graph of is the graph of first stretched __________ by a factor of ___, then reflected in the _______, and finally translated ________ units and ________ units. vertically left 3 x-axis up 2

  4. 2.4 Use Absolute Value Functions and Transformations Checkpoint. Complete the following exercise. • Graph the function . Compare the graph with the graph . Vertical shrink with scale factor of ½. Reflect over the x-axis. Translated right 1 and down 2. Increasing x < 1 Decreasing x > 1

  5. 2.4 Use Absolute Value Functions and Transformations Write an absolute value function. Example 2 Write a function for the graph shown. Solution The vertex of the graph is ( ___, ___ ). So, the equation has the form Substitute the coordinates of the point ( ___, ___ ) into the equation and solve for a. Substitute for x and for y. Solve for a. An equation for the graph is y = _______________

  6. 2.4 Use Absolute Value Functions and Transformations Checkpoint. Write a function for the graph shown.

  7. 2.4 Use Absolute Value Functions and Transformations Apply transformations to a graph Example 3 The graph of a function y = f(x) is shown. Sketch the graph of the given function. Solution • The graph of is the graph of shrunk _________ by a factor of ____. vertically ½ ½ To draw the graph, find ___ y for each labeled point ( x, y ) on the graph of f(x). Plot the points ( x, __ y ) and connect them. ½

  8. 2.4 Use Absolute Value Functions and Transformations Apply transformations to a graph Example 3 The graph of a function y = f(x) is shown. Sketch the graph of the given function. Solution • The graph of is the graph of _________ in the x-axis, then translated _______ unit and ______ units. reflected right 1 up 2 To draw the graph, first reflect the labeled points then translate and connect their images.

  9. 2.4 Use Absolute Value Functions and Transformations Checkpoint. Use the graph of f(x) in Example 3 to graph the given equation.

  10. 2.4 Use Absolute Value Functions and Transformations Pg. 44, 2.4 #1-24

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