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# Gr10 piecewise functions

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## Gr10 piecewise functionsPresentation Transcript

• Algebra II Piecewise Functions Edited by Mrs. Harlow
• 2-6: Special Functions
• Constant
• Identity
• Absolute Value
• Step/Greatest Integer
• Piecewise
• Constant Function: A linear function in the form y = b. y = 3
• Identity Function: A linear function in the form y = x. y=x
• Up to now, we’ve been looking at functions represented by a single equation.
• In real life, however, functions are represented by a combination of equations, each corresponding to a part of the domain.
• These are called piecewise functions.
• One equation gives the value of f (x) when x ≤ 1
• And the other when x>1
• Evaluate f(x) when x=0, x=2, x=4
• First you have to figure out which equation to use
• You NEVER use both
X=0 This one fits into the top equation So: 0+2=2 f(0)=2 X=2 This one fits here So: 2(2) + 1 = 5 f(2) = 5 X=4 This one fits here So: 2(4) + 1 = 9 f(4) = 9
• Graph:
• For all x’s < 1, use the top graph (to the left of 1)
• For all x’s ≥ 1, use the bottom graph (to the right of 1)
• x=1 is the breaking point of the graph. To the left is the top equation. To the right is the bottom equation.
• Graph:
• Greatest Integer Function: A function in the form y = [ x ]
• Note: [ x ] means the greatest integer less than or equal to x . For example, the largest integer less than or equal to -3.5 is -4.
2 4 6 – 2 – 4 – 6 x 2 4 6 – 2 – 4 – 6 y y =[ x ]
• Greatest Integer Function: A function inthe form y = [ x ]
• Graph y = [ x ] + 2 by completing the t-table:
x y -3 - 2.75 -2.5 -2.25 -2 -1.75 -1.5 -1.25 -1 0 1 2 4 6 – 2 – 4 – 6 x 2 4 6 – 2 – 4 – 6 y x y -3 y = [-3]+2=-1 - 2.75 y = [-2.75]+2=-1 -2.5 y = [-2.5]+2=-1 -2.25 y = [-2.25]+2=-1 -2 y = [-2]+2 =0 -1.75 y = [-1.75]+2=0 -1.5 y = [-1.5]+2=0 -1.25 y = [-1.25]+2=0 -1 y = [-1]+2=1 0 y = [0]+2=2 1 y = [1]+2=3
• Step Functions
•
• Graph :
•
• Labor costs at the Fix-It Auto Repair Shop are \$60 per hour or any fraction thereof. Draw a graph that represents this situation.
• Assignment