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Types of Piecewise functions

Types of Piecewise functions. Step Functions: functions made up of Horizontal line segments with a closed circle on one end and an open circle on the other. The graph looks like a set of steps Absolute Value Functions: V-shaped grapg. Absolute Value Function- V- Shaped graph.

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Types of Piecewise functions

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  1. Types of Piecewise functions • Step Functions: • functions made up of Horizontal line segments with a closed circle on one end and an open circle on the other. • The graph looks like a set of steps Absolute Value Functions: V-shaped grapg

  2. Absolute Value Function- V- Shaped graph.

  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

  4. Write absolute value function as a piecewise function

  5. Graphing Absolute Value functions f(x) = a |x - h| + k • Vertex is (h,k) • AOS: x=h • If a< 0 the graph opens down (a is negative) • If a>0 the 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)

  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 @ (0,-3) • It has the form: • y = a |x - 0| - 3 • To find a: substitute the coordinate of a point (2,1) in and solve • (or count the slope from the vertex to another point to the right) • Remember: a is positive if the graph goes up • a is negative if the graph goes down So the equation is: y = 2|x| -3

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