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3.4 Absolute Value Functions

3.4 Absolute Value Functions. Absolute Value is defined by:. The graph of this piecewise function consists of 2 rays, is V-shaped and opens up. To the left of x=0 the line is y = -x. To the right of x = 0 the line is y = x. Notice that the graph is symmetric in the y-axis because

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3.4 Absolute Value Functions

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  1. 3.4 Absolute Value Functions

  2. Absolute Value is defined by:

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

  4. y = a |x - h| + k • Vertex is at (h,k) & is symmetrical in the line x=h • V-shaped • If a < 0 the graph opens down (a is negative) • If a > 0the graph opens up (a is positive) • The graph is wider if |a| < 1 (fraction < 1) • The graph is narrower if |a| > 1 • a is the slope to the right ofthe vertex (…-a is the slope to the left of the vertex)

  5. To graph y = a |x - h| + k • Plot the vertex (h,k) • Set what’s in the absolute value symbols to 0 and solving for x, gives you the x-coordinate of the vertex. The y-coordinate is k. • Use the slope to plot another point to the RIGHT of the vertex. • Use symmetry to plot a 3rd point • Complete the graph

  6. Graph y = -|x + 2| + 3 • V = (-2,3) • Apply the slope a=-1 to that point • Use the line of symmetry x=-2 to plot the 3rd point. • Complete the graph

  7. Graph y = -|x - 1| + 1

  8. Write the equation for:

  9. The vertex is at (0, -3) • The equation needs to be in the form • y = a | x – h | + k • Therefore, y = a | x – 0 | - 3 • Find the slope to the right of the vertex to • find ‘a’. • The equation is: y = 2 | x – 0 | - 3 So the equation is: y = 2|x| -3

  10. Write the equation for: y = ½|x| + 3

  11. Assignment -Absolute Value Worksheet 1

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