Page 848 - Algebra 1

APPENDIX
L E2S S O N Graphing Piecewise and Step Functions
New Concepts
When a function has a different rule for different pieces of its domain, it is called a piecewise function. This kind of function is a combination of two or more functions. It assigns a different value to each domain interval. A piecewise function that is constant for each part of the domain is called a step function.
Evaluating a Step Function
Evaluate the function for x = -4, x = -2, and x = 6. f(x)=⎨⎧10if x≤-2
⎩8if x>-2 SOLUTION
When x = -4, then f(-4) = 10 because -4 ≤ -2. When x = -2, then f(-2) = 10 because -2 ≤ -2. When x = 6, then f(6) = 8 because 6 > -2.
Evaluating a Piecewise Function
Evaluate the function for x = -4, x = -2, and x = 6. f(x)=⎨⎧2x-1 if x<6
⎩8x2 if x ≥ 6 SOLUTION
Whenx=-4,thenx<6.Usethepieceof thefunction, f(x)=2x-1.
Example
1
Example
2
f(-4) = 2(-4) - 1 = -8 - 1
Substitute -4 for x into f(x). Multiply 2 and -4. Simplify.
= -9
Whenx=-2,thenx<6.Usethepieceof thefunction, f(x)=2x-1.
f(-2) = 2(-2) - 1 = -4 - 1
Substitute -2 for x into f(x). Multiply 2 and -2.
Simplify.
= -5
When x = 6, then x ≥ 6. Use the piece of the function, f(x) = 8x2.
f(6) = 8 · 62 = 8 · 36
= 288
Substitute 6 for x into f(x). Simplify the exponent. Multiply.
Appendix Lesson 2 833
APPENDIX LESSONS