Vocab
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.
f(x)={x+32xif x<0if x≥0
Questions:
a) What is f(−2)f(−2)?
f(−2)=1f(−2)=1
A piecewise function is made up how many functions?
Two or More formulas
f(x)={2x+1x2if x<0if x≥0
Questions:
a) What is f(−3)f(−3)?
f(−3)=−5f(−3)=−5
g(x)={x2−13x+2if x<1if x≥1
Questions:
c) What is g(5)g(5)?
g(5)=17g(5)=17
What is a interval?
A specific range of input values (usually x-values) over which a particular rule or expression applies.
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
Each formula applies to a specific part of the...
domain
f(x)={2x+1x2if x<0if x≥0
Questions:
b) What is f(0)f(0)?
f(0)=0f(0)=0
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
What is domain?
The set of all possible input values (x-values) for which the function is defined
f(x)={ x+3 2x if x<0 if x≥0
Questions: What is f ( 4 ) f(4)?
answer: f(4)=8f(4)=8
Look at the input value.
Choose the piece whose ... includes that value.
interval
f(x)={2x+1x2if x<0if x≥0
Questions:
c) What is f(4)f(4)?
f(4)=16
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
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.
f(x)={x2−13x−4if x<2if x≥2
a) What is f(1)f(1)?
Answer: f(1)=0f(1)=0
Graph each rule only on its...
valid interval
g(x)={x2−13x+2if x<1if x≥1
Questions:
a) What is g(−2)g(−2)?
g(−2)=3
h(x)=⎩⎨⎧x+2−2xx2−4if x<−1if −1≤x<2if x≥2
Questions:
c) What is h(3)h(3)?
h(3)=5
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
f(x)={x2−13x−4if x<2if x≥2
b) What is f(2)f(2)?
f(2)=2
For any input value x, .... is used, never more than one. How many expressions are used?
only one expression
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
f(x)=⎩⎨⎧3x−4x2+12x−5if x<1if 1≤x<3if x≥3
Questions:
a) What is f(0)f(0)?
f(0)=−4