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Piecewise Functions
Related Topics
Wize University Calculus 1 Textbook > Pre-Calculus (Review)
Piecewise Functions
3 Activities
Practice: Piecewise Functions
The graph shown below is the graph of the piecewise function
f
(
x
)
f(x)
f
(
x
)
.
Select the following statements that are true about
f
(
x
)
f(x)
f
(
x
)
.
A) The domain of
f
(
x
)
f(x)~
f
(
x
)
is
[
−
4
,
10
]
[-4,10]
[
−
4
,
10
]
B) The domain of
f
(
x
)
f(x)~
f
(
x
)
is
[
−
4
,
0
]
∪
[
1
,
4
]
∪
[
5
,
10
]
[-4,0]~\cup~[1,4]~\cup~[5,10]
[
−
4
,
0
]
∪
[
1
,
4
]
∪
[
5
,
10
]
C)
f
(
x
)
f(x)
f
(
x
)
is discontinuous between
(
0
,
1
)
(0,1)
(
0
,
1
)
and
(
4
,
5
)
(4,5)
(
4
,
5
)
D)
f
(
x
)
=
{
−
x
2
;
−
4
<
x
<
0
−
3
x
+
1
;
1
<
x
<
4
1
5
x
5
<
x
<
10
f(x)=\begin{cases} -x^2;&-4<{x}<0\\ -3x+1;&1<x<4\\ \frac{1}{5}x&5<x<10 \end{cases}
f
(
x
)
=
⎩
⎨
⎧
−
x
2
;
−
3
x
+
1
;
5
1
x
−
4
<
x
<
0
1
<
x
<
4
5
<
x
<
10
E)
f
(
x
)
=
{
−
x
2
;
−
4
≤
x
≤
0
−
3
x
+
1
;
1
≤
x
≤
4
1
5
x
5
≤
x
≤
10
f(x)=\begin{cases} -x^2;&-4\leq{x}\leq{0}\\ -3x+1;&1\leq{x}\leq{4}\\ \frac{1}{5}x&5\leq{x}\leq{10} \end{cases}
f
(
x
)
=
⎩
⎨
⎧
−
x
2
;
−
3
x
+
1
;
5
1
x
−
4
≤
x
≤
0
1
≤
x
≤
4
5
≤
x
≤
10
I don't know
Check Submission
More Piecewise Functions Questions:
Continuity and Piecewise Functions
What values of
a
a
a
and
b
b
b
make the following function
continuous
?
f
(
x
)
=
{
a
x
2
−
4
;
x
<
−
2
a
x
+
b
;
−
2
≤
x
≤
3
a
x
2
+
b
x
+
10
;
x
>
3
f(x)= \begin{cases} ax^2-4;&&x<-2\\\\ ax+b;&&-2\leq{}x\leq3\\\\ ax^2+bx+10;&&x>3 \end{cases}
f
(
x
)
=
⎩
⎨
⎧
a
x
2
−
4
;
a
x
+
b
;
a
x
2
+
b
x
+
10
;
x
<
−
2
−
2
≤
x
≤
3
x
>
3
Piecewise Functions
Practice: Piecewise Functions
What value of 'a' would make the following piecewise function
continuous
?
f
(
x
)
=
{
x
2
+
10
;
x
<
1
−
x
+
7
a
;
x
≥
1
f(x)=\begin{cases} x^2+10;&x<1\\ -x+7a;&x\geq1 \end{cases}
f
(
x
)
=
{
x
2
+
10
;
−
x
+
7
a
;
x
<
1
x
≥
1
Piecewise Functions
Practice: Piecewise Functions
What value of 'a' would make the following piecewise function
continuous
?
f
(
x
)
=
{
−
2
x
2
+
7
;
x
<
−
4
3
x
+
a
;
x
≥
−
4
f(x)=\begin{cases} -2x^2+7;&x<-4\\ 3x+a;&x\geq-4 \end{cases}
f
(
x
)
=
{
−
2
x
2
+
7
;
3
x
+
a
;
x
<
−
4
x
≥
−
4
Piecewise Functions
Practice: Piecewise Functions
Chelsea makes wooden boards and sells them to restaurants. She charges $20/board for the first 25 boards. After the first 25 boards purchased up to 50 boards, the price of the board drops by $5.00/board. After Chelsea sells 50 boards to the restaurant, the price will decrease to $12.50/board.
Determine a function that models this situation.
Piecewise Functions
Practice: Piecewise Functions
Leonard is purchasing boxes from a wholesaler for his cosmetic company. The wholesaler sells the first 1000 boxes for $2.50/box. The next 5000 boxes are sold at $2.00/box and any number of boxes purchased beyond this are sold for $1.75/box.
Determine a function that models this situation.
Piecewise Functions
Practice: Piecewise Functions
The graph shown below is the graph of the piecewise function
f
(
x
)
f(x)
f
(
x
)
.
Select the following statements that are true about
f
(
x
)
f(x)
f
(
x
)
.
Piecewise Functions
Practice: Piecewise Functions
The graph shown below is the graph of the piecewise function
f
(
x
)
f(x)
f
(
x
)
.
Select the following statements that are true about
f
(
x
)
f(x)
f
(
x
)
.
Piecewise Functions
Practice: Piecewise Functions
The graph shown below is the graph of the piecewise function
f
(
x
)
f(x)
f
(
x
)
.
Select the following statements that are true about
f
(
x
)
f(x)
f
(
x
)
.
Piecewise Functions
The graph shown below is the graph of the piecewise function
f
(
x
)
f(x)
f
(
x
)
.
Select the following statements that are true about
f
(
x
)
f(x)
f
(
x
)
.
Piecewise Functions
The following graph is of
y
=
b
[
[
c
x
]
]
y=b[[cx]]
y
=
b
[[
c
x
]]
(Where [[ ]] denotes the greatest integer.) What are b and c?
