Name:
Date:
Piecewise Functions and Their Graphs
Piecewise Functions:
Example 1:
Graph the following piecewise function:
−𝒙 + 𝟒,
𝒙 < −𝟑
𝒇 𝒙 =
𝟐𝒙,
𝒙 ≥ −𝟑
Evaluate the following:
𝒇 −𝟓 =
𝒇 −𝟑
𝒇(𝟐)
Example 1:
Graph the following piecewise function:
𝒙𝟐 − 𝟏
𝒙≤𝟐
𝒇 𝒙 = 𝒙+𝟒
𝟐≤𝒙≤𝟓
−𝟑
𝒙>𝟓
Evaluate the following:
𝒇 −𝟓 =
𝒇 −𝟑
𝒇(𝟐)
Period:
1.
⎧⎪x + 5
f (x ) = ⎨ 2
⎪⎩x + 2x + 3
x < −2
x ≥ −2
f (3) =
f (−4 ) =
f (−2 ) =
2.
⎧⎪2x + 1
f (x ) = ⎨ 2
⎪⎩x + 3
f (−2 ) =
f (6 ) =
f (1 ) =
x ≥1
x <1
3.
⎧−2x + 1
f (x ) = ⎨
⎩5x − 4
x ≤2
x >2
f (−4 ) =
f (8 ) =
f (2 ) =
4.
⎧x 2 − 1
⎪
f (x ) = ⎨2x − 1
⎪3
⎩
f (−2 ) =
f (0 ) =
f (5 ) =
x ≤0
0<x ≤5
x >5
5.
⎧x 2
⎪⎪
f x = ⎨7
⎪−x 2 + 4
⎪⎩
()
x <0
x =0
x >0
f (−4 ) =
f (0 ) =
f (3) =
6.
⎧5
x ≤ −4
⎪⎪
f x = ⎨x − 3 − 4 ≤ x ≤ −2
⎪−2x − 3
x > −2
⎪⎩
()
f (−4 ) =
f (0 ) =
f (3) =