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Graphing Absolute Value Functions using Transformations

Graphing Absolute Value Functions using Transformations. Vocabulary. The function f(x) = |x| is an absolute value function. The graph of this piecewise function consists of 2 rays, is v-shaped, and opens up. to the right of x = 0 the line is y = x. to the left of x = 0 the line is

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Graphing Absolute Value Functions using Transformations

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  1. Graphing Absolute Value Functions using Transformations

  2. Vocabulary The function f(x) = |x| is an absolute value function.

  3. The graph of this piecewise function consists of 2 rays, is v-shaped, and opens up. to the right of x = 0 the line is y = x to the left of x = 0 the line is y = -x Notice that the graph is symmetric across the y-axis because for every point (x,y) on the graph, the point (-x,y) is also on the graph.

  4. Vocabulary • The highest or lowest point on the graph of an absolute value function is called the vertex. • The axis of symmetryof the graph of a function is a vertical line that divides the graph into mirror images.

  5. Absolute Value Function • Vertex • Axis of Symmetry

  6. Vocabulary • The zeros of a function f(x) are the values of x that make the value of f(x) equal to 0. On this graph, f(x) (or y) is 0 when x = -3 and x = 3. f(x) = |x| - 3

  7. Vocabulary • A transformation changes a graph’s size, shape, position, or orientation. • A translation is a transformation that shifts a graph horizontally and/or vertically, but does not change its size, shape, or orientation. • A reflection is when a graph is flipped over a line. A graph flips vertically when -1.f(x) and it flips horizontally when f(-1x).

  8. Vocabulary • Adilationchanges the size of a graph by stretching or compressing it. This happens when you multiply the function by a number.

  9. Transformations y = -a |x – h| + k remember that (h, k) is your vertex reflection across the x-axis vertical translation vertical stretcha > 1(makes it narrower)ORvertical compression 0 < a < 1 (makes it wider) horizontal translation (opposite of h)

  10. Example 1 Identify the transformations. • y = 3 |x + 2| - 3 • y = |x – 1| + 2 • y = 2 |x + 3| - 1 • y = -1/3|x – 2| + 1

  11. Example 2 Graph y = -2 |x + 3| + 2. • What is the vertex? • What are the intercepts?

  12. You Try: Graph y = -1/2 |x – 1| - 2 compare the graph with the graph of y = |x| What are the transformations?

  13. Example 3 Write a function for the graph shown.

  14. You Try: Write a function for the graph shown.

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