How do I graph and write absolute value

• How do I graph and write absolute value functions?

2. 4 Use Absolute Value Functions and Transformations Example 1 Graph a function of the form . Graph. Identify the intercepts, zeros, and intervals of increase and decrease. Compare the graph with the graph. 1. Identify and plot the vertex, 2. Plot another point on the graph such as Use symmetry to plot a third point, V-shaped 3. Connect the points with a ______ graph. 4. Examine the graph. The x-intercepts are ____ and ____, which are also the _______ zeros of the function, and the yintercept is ____. The function is increasing when _____ and decreasing when ____.

2. 4 Use Absolute Value Functions and Transformations Example 1 Graph a function of the form Graph. Identify the intercepts, zeros, and intervals of increase and decrease. Compare the graph with the graph. 5. Compare with of of . The graph is the graph vertically by first stretched _____ a factor of ___, then reflected in the left 3 _______, x-axis and finally translated ____ up 2 units and ____ .

2. 4 Use Absolute Value Functions and Transformations Checkpoint. Complete the following exercise. 1. Graph the function 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 . Compare the graph with

2. 4 Use Absolute Value Functions and Transformations Example 2 Write an absolute value function. 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 = ________

2. 4 Use Absolute Value Functions and Transformations Checkpoint. Write a function for the graph shown. 2.

2. 4 Use Absolute Value Functions and Transformations Example 3 Apply transformations to a graph The graph of a function y = f(x) is shown. Sketch the graph of the given function. Solution a. The graph of of is the graph shrunk vertically _____ by a factor of ____. ½ To draw the graph, find ___ ½ y for each labeled point ( x, y ) on the graph of f(x). Plot the points ( x, __ ½ y ) and connect them.

2. 4 Use Absolute Value Functions and Transformations Example 3 Apply transformations to a graph The graph of a function y = f(x) is shown. Sketch the graph of the given function. Solution b. The graph of is the reflected in the x_____ axis, then translated _______ right 1 unit and up 2 units. ______ To draw the graph, first reflect the labeled points then translate and connect their images.