Piecewise Function

Vocab

100

What is a piecewise function?

A piecewise function is a function that is defined by different expressions depending on the input value (usually xx). Each piece of the function applies to a specific interval of the domain.

200

What is a interval?

A specific range of input values (usually x-values) over which a particular rule or expression applies.

300

What is domain?

The set of all possible input values (x-values) for which the function is defined

400

What is a closed interval? 

Includes the endpoint (e.g., x≤3x≤3 or x≥0x≥0); shown with a solid dot on a graph.

500

What is a open interval?

Does not include the endpoint (e.g., x<3x<3 or x>0x>0); shown with a hollow dot on a graph

Question 1

100

f(x)={x+32xif x<0if x≥0

Questions:

• a) What is f(−2)f(−2)?

f(−2)=1f(−2)=1

200

f(x)={ x+3 2x if x<0 if x≥0  

Question: b) What is f ( 0 ) f(0)?

Answer: f(0)=0f(0)=0

300

f(x)={ x+3 2x if x<0 if x≥0  

Questions: What is f ( 4 ) f(4)?

answer: f(4)=8f(4)=8

400

f(x)={x2−13x−4if x<2if x≥2

a) What is f(1)f(1)?

Answer: f(1)=0f(1)=0

500

f(x)={x2−13x−4if x<2if x≥2

b) What is f(2)f(2)?

f(2)=2

rules

100

A piecewise function is made up how many functions?

Two or More formulas

200

Each formula applies to a specific part of the...

domain 

300

• Look at the input value.

• Choose the piece whose ... includes that value.

interval 

400

Graph each rule only on its...

valid interval 

500

For any input value x, .... is used, never more than one. How many expressions are used?

only one expression

Question 2

100

f(x)={2x+1x2if x<0if x≥0

Questions:

a) What is f(−3)f(−3)?

f(−3)=−5f(−3)=−5

200

f(x)={2x+1x2if x<0if x≥0

Questions:

b) What is f(0)f(0)?

f(0)=0f(0)=0

300

f(x)={2x+1x2if x<0if x≥0

Questions:

c) What is f(4)f(4)?

f(4)=16

400

g(x)={x2−13x+2if x<1if x≥1

Questions:

a) What is g(−2)g(−2)?

g(−2)=3

500

g(x)={x2−1if x<13x+2if x≥1g(x)={x2−13x+2if x<1if x≥1

Questions:

b) What is g(1)g(1)?

g(1)=5

Question 3

100

g(x)={x2−13x+2if x<1if x≥1

Questions:

c) What is g(5)g(5)?

g(5)=17g(5)=17

200

h(x)=⎩⎨⎧x+2−2xx2−4if x<−1if −1≤x<2if x≥2

Questions:

a) What is h(−3)h(−3)?

h(−3)=−1h(−3)=−1

300

h(x)=⎩⎨⎧x+2−2xx2−4if x<−1if −1≤x<2if x≥2

Questions:

b) What is h(0)h(0)?

h(0)=0h(0)=0

400

h(x)=⎩⎨⎧x+2−2xx2−4if x<−1if −1≤x<2if x≥2

Questions:

c) What is h(3)h(3)?

h(3)=5

500

f(x)=⎩⎨⎧3x−4x2+12x−5if x<1if 1≤x<3if x≥3

Questions:

a) What is f(0)f(0)?

f(0)=−4