Piecewise Functions

Vocabulary

100

The set of all input values

What is a Domain?

200

What is the Range of a function?

All possible output values.

300

What is the "2x + 1" in f(x) = 2x + 1 called?

The rule of the function.

400

What is the "f" in f(x) = 2x + 1 called?

The name of the function.

500

A function with one or more rules each with a specified and limited domain is called:

A Piecewise Function

Find the Output

100

f(x) =  -3x,         if x<0

           2x + 10,  if x>0

Find f(11)

f(11) = 32

200

f(x) =  -3x,         if x<0

           2x + 10,  if x>0

Find f(-1)

f(-1) = 3

300

f(x) =  -3x,         if x<0

           2x + 10,  if x>0

Find f(0)

No solution

400

g(x) = 2x + 1, if x>2

          -x - 4,   if x<2

Find g(-21)

g(-21) = 17

500

f(x) =  8x + 3,      if x > 2

           (1/2)x - 1, if x < 2 

Find f(-5).

f(-5) = -7/2

Find the Output 2

100

f(t) = -|t + 4| + 6; Find f(10)

f(10) = -8

200

h(k) = -2k² + 4; Find h(8).

h(8) = -124

300

g(x) = 2x + 1, if x>2

          -x - 4,   if x<2

Find g(1)

g(1) = -5

400

m(r) = 3(r + 4) + 2; Find m(12)

m(12) = 50

500

f(x) =  8x + 3,      if x > 2

           (1/2)x - 1, if x < 2 

Find f(5).

f(5) = 43

Find the Input

100

h(k) = -2k + 4

Find k if h(k) = -28

k = 16

200

f(x) =  -3x

Find x if f(x) = 1

x = -1/3

300

g(x) = 2x + 1

Find x if g(x) = 0

x = -1/2

400

f(x) =  8x + 3

Find x if f(x) = 10

x = 7/8

500

f(x) = (x)(x)(x)

Find x if f(x) = -8

x = -2