Piecewise Functions

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Piecewise Functions

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Piecewise Functions

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Piecewise Functions

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Piecewise Functions

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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 [−5,12][-5,12][−5,12] and the range is [−14,8][-14,8][−14,8]. 

B) The domain of f(x) f(x)~f(x) is (−5,12)(-5,12)(−5,12) and the range is (−14,8)(-14,8)(−14,8). 

C) The domain of f(x) f(x)~f(x) is [−5,−1] ∪ [0,12][-5,-1]~\cup~[0,12][−5,−1] ∪ [0,12] and the range is [−14,8][-14,8][−14,8].  

D) The domain of f(x) f(x)~f(x) is (−5,−1) ∪ (0,12)(-5,-1)~\cup~(0,12)(−5,−1) ∪ (0,12) and the range is (−14,8)(-14,8)(−14,8).   

F)f(x)={(x+4)2−1;−5≤x≤−1−4x+8;−1≤x≤4−∣x−5∣−74≤x≤12f(x)=\begin{cases}
(x+4)^2-1;&-5\leq{x}\leq{-1}\\
-4x+8;&-1\leq{x}\leq{4}\\
-|x-5|-7&4\leq{x}\leq{12}
\end{cases}f(x)=⎩⎨⎧​(x+4)2−1;−4x+8;−∣x−5∣−7​−5≤x≤−1−1≤x≤44≤x≤12​ 

G) f(x)={(x+4)2−1;−5<x<−1−4x+8;−1<x<4−∣x−5∣−74<x<12f(x)=\begin{cases}
(x+4)^2-1;&-5<x<-1\\
-4x+8;&-1<x<4\\
-|x-5|-7&4<x<12
\end{cases}f(x)=⎩⎨⎧​(x+4)2−1;−4x+8;−∣x−5∣−7​−5<x<−1−1<x<44<x<12​ 

E) There is a discontinuity at x=−1x=-1x=−1.

I don't know

Continuity and Piecewise Functions

What values of aaa and bbb make the following function continuous? 
f(x)={ax2−4;x<−2ax+b;−2≤x≤3ax2+bx+10;x>3f(x)=
\begin{cases}
ax^2-4;&&x<-2\\\\
ax+b;&&-2\leq{}x\leq3\\\\
ax^2+bx+10;&&x>3
\end{cases}f(x)=⎩⎨⎧​ax2−4;ax+b;ax2+bx+10;​​x<−2−2≤x≤3x>3​

Piecewise Functions

Practice: Piecewise Functions
What value of 'a' would make the following piecewise function continuous?
f(x)={x2+10;x<1−x+7a;x≥1f(x)=\begin{cases}
x^2+10;&x<1\\
-x+7a;&x\geq1
\end{cases}f(x)={x2+10;−x+7a;​x<1x≥1​

Piecewise Functions

Practice: Piecewise Functions
What value of 'a' would make the following piecewise function continuous?
f(x)={−2x2+7;x<−43x+a;x≥−4f(x)=\begin{cases}
-2x^2+7;&x<-4\\
3x+a;&x\geq-4
\end{cases}f(x)={−2x2+7;3x+a;​x<−4x≥−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
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).

Continuity and Piecewise Functions

What values of aaa and bbb make the following function continuous? 
f(x)={ax2−4;x<−2ax+b;−2≤x≤3ax2+bx+10;x>3f(x)=
\begin{cases}
ax^2-4;&&x<-2\\\\
ax+b;&&-2\leq{}x\leq3\\\\
ax^2+bx+10;&&x>3
\end{cases}f(x)=⎩⎨⎧​ax2−4;ax+b;ax2+bx+10;​​x<−2−2≤x≤3x>3​

Piecewise Functions

Practice: Piecewise Functions
What value of 'a' would make the following piecewise function continuous?
f(x)={x2+10;x<1−x+7a;x≥1f(x)=\begin{cases}
x^2+10;&x<1\\
-x+7a;&x\geq1
\end{cases}f(x)={x2+10;−x+7a;​x<1x≥1​

Piecewise Functions

Practice: Piecewise Functions
What value of 'a' would make the following piecewise function continuous?
f(x)={−2x2+7;x<−43x+a;x≥−4f(x)=\begin{cases}
-2x^2+7;&x<-4\\
3x+a;&x\geq-4
\end{cases}f(x)={−2x2+7;3x+a;​x<−4x≥−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).

Continuity and Piecewise Functions

What values of aaa and bbb make the following function continuous? 
f(x)={ax2−4;x<−2ax+b;−2≤x≤3ax2+bx+10;x>3f(x)=
\begin{cases}
ax^2-4;&&x<-2\\\\
ax+b;&&-2\leq{}x\leq3\\\\
ax^2+bx+10;&&x>3
\end{cases}f(x)=⎩⎨⎧​ax2−4;ax+b;ax2+bx+10;​​x<−2−2≤x≤3x>3​

Piecewise Functions

Practice: Piecewise Functions
What value of 'a' would make the following piecewise function continuous?
f(x)={x2+10;x<1−x+7a;x≥1f(x)=\begin{cases}
x^2+10;&x<1\\
-x+7a;&x\geq1
\end{cases}f(x)={x2+10;−x+7a;​x<1x≥1​

Piecewise Functions

Practice: Piecewise Functions
What value of 'a' would make the following piecewise function continuous?
f(x)={−2x2+7;x<−43x+a;x≥−4f(x)=\begin{cases}
-2x^2+7;&x<-4\\
3x+a;&x\geq-4
\end{cases}f(x)={−2x2+7;3x+a;​x<−4x≥−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).

Continuity and Piecewise Functions

What values of aaa and bbb make the following function continuous? 
f(x)={ax2−4;x<−2ax+b;−2≤x≤3ax2+bx+10;x>3f(x)=
\begin{cases}
ax^2-4;&&x<-2\\\\
ax+b;&&-2\leq{}x\leq3\\\\
ax^2+bx+10;&&x>3
\end{cases}f(x)=⎩⎨⎧​ax2−4;ax+b;ax2+bx+10;​​x<−2−2≤x≤3x>3​

Piecewise Functions

Practice: Piecewise Functions
What value of 'a' would make the following piecewise function continuous?
f(x)={x2+10;x<1−x+7a;x≥1f(x)=\begin{cases}
x^2+10;&x<1\\
-x+7a;&x\geq1
\end{cases}f(x)={x2+10;−x+7a;​x<1x≥1​

Piecewise Functions

Practice: Piecewise Functions
What value of 'a' would make the following piecewise function continuous?
f(x)={−2x2+7;x<−43x+a;x≥−4f(x)=\begin{cases}
-2x^2+7;&x<-4\\
3x+a;&x\geq-4
\end{cases}f(x)={−2x2+7;3x+a;​x<−4x≥−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[[cx]]y=b[[cx]]y=b[[cx]] (Where [[ ]] denotes the greatest integer.) What are b and c?

Piecewise Functions

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