Piecewise Functions
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Question 1 of 4
1. Question
Graph the function$$f(x)=\begin{cases}2x+1, x<-1\\1-x^2,x≥-1\end{cases}$$Hint
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PieceWise functions are a set of functions that share a common pointUse a table of values and test several values of `x` to get the value of `y``x` `-2` `-1` `0` `1` `2` `y` Substitute the values of `x` to the respective functions to get their `y` values`f(x)` `=` $$\begin{cases}2x+1, x<-1\\1-x^2,x≥-1\end{cases}$$ `x=-2``f(x)` `=` `2x+1` 1st function `f(-2)` `=` `2(-2)+1` `=` `-4+1` `=` `-3` `x=-1``f(x)` `=` `2x+1` 1st function `f(-1)` `=` `2(-1)+1` `=` `-2+1` `=` `-1` `f(x)` `=` `1-x^2` 2nd function `f(-1)` `=` `1-(-1)^2` `=` `1-1` `=` `0` `x=0``f(x)` `=` `1-x^2` 2nd function `f(0)` `=` `1-(0)^2` `=` `1` `x=1``f(x)` `=` `1-x^2` 2nd function `f(1)` `=` `1-(1)^2` `=` `1-1` `=` `0` `x=2``f(x)` `=` `1-x^2` 2nd function `f(2)` `=` `1-(2)^2` `=` `1-4` `=` `-3` `x` `-2` `-1` `0` `1` `2` `y` `-3` `-1,0` `1` `0` `-3` Next, plot the points on the graph.Use empty dots for less than (`<`) values and filled dots for greater than or equal (`≥`) values
Finally, form the curve by connecting the points
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Question 2 of 4
2. Question
Graph the function$$f(x)=\begin{cases}x^2, x≤0\\[0.3em] \frac{1}{2}x,x>0\end{cases}$$Hint
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PieceWise functions are a set of functions that share a common pointUse a table of values and test several values of `x` to get the value of `y``x` `-2` `-1` `0` `1` `2` `y` Substitute the values of `x` to the respective functions to get their `y` values`f(x)` `=` $$\begin{cases}x^2, x≤0\\[0.3em] \frac{1}{2}x,x>0\end{cases}$$ `x=-2``f(x)` `=` `x^2` 1st function `f(-2)` `=` `(-2)^2` `=` `4` `x=-1``f(x)` `=` `x^2` 1st function `f(-1)` `=` `(-1)^2` `=` `1` `x=0``f(x)` `=` `x^2` 1st function `f(0)` `=` `0^2` `=` `0` `f(x)` `=` `1/2x` 2nd function `f(0)` `=` `1/2(0)` `=` `0` `x=1``f(x)` `=` `1/2x` 2nd function `f(1)` `=` `1/2(1)` `=` `1/2` `x=2``f(x)` `=` `1/2x` 2nd function `f(2)` `=` `1/2(2)` `=` `1` `x` `-2` `-1` `0` `1` `2` `y` `4` `1` `0,0` `1/2` `1` Next, plot the points on the graph.Use empty dots for greater than (`>`) values and filled dots for less than or equal (`≤`) values
Finally, form the curve by connecting the points
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Question 3 of 4
3. Question
Graph the function$$f(x)=\begin{cases}x^2, x≤1\\[0.3em] 2-x,x>1\end{cases}$$Hint
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Keep Going!
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PieceWise functions are a set of functions that share a common pointUse a table of values and test several values of `x` to get the value of `y``x` `-2` `-1` `0` `1` `2` `y` Substitute the values of `x` to the respective functions to get their `y` values`f(x)` `=` $$\begin{cases}x^2, x≤1\\[0.3em] 2-x,x>1\end{cases}$$ `x=-2``f(x)` `=` `x^2` 1st function `f(-2)` `=` `(-2)^2` `=` `4` `x=-1``f(x)` `=` `x^2` 1st function `f(-1)` `=` `(-1)^2` `=` `1` `x=0``f(x)` `=` `x^2` 1st function `f(-1)` `=` `(0)^2` `=` `0` `x=1``f(x)` `=` `x^2` 1st function `f(1)` `=` `1^2` `=` `1` `f(x)` `=` `2-x` 2nd function `f(0)` `=` `2-1` `=` `1` `x=2``f(x)` `=` `2-x` 2nd function `f(2)` `=` `2-2` `=` `0` `x` `-2` `-1` `0` `1` `2` `y` `4` `1` `0` `1,1` `0` Next, plot the points on the graph.Use empty dots for greater than (`>`) values and filled dots for less than or equal (`≤`) values
Finally, form the curve by connecting the points
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Question 4 of 4
4. Question
Graph the function$$f(x)=\begin{cases}x^2, x≤1\\[0.3em] x-1,x>1\end{cases}$$Hint
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PieceWise functions are a set of functions that share a common pointUse a table of values and test several values of `x` to get the value of `y``x` `-1` `0` `1` `2` `3` `y` Substitute the values of `x` to the respective functions to get their `y` values`f(x)` `=` $$\begin{cases}x^2, x≤1\\[0.3em] x-1,x>1\end{cases}$$ `x=-1``f(x)` `=` `x^2` 1st function `f(-1)` `=` `(-1)^2` `=` `1` `x=0``f(x)` `=` `x^2` 1st function `f(-1)` `=` `(0)^2` `=` `0` `x=1``f(x)` `=` `x^2` 1st function `f(1)` `=` `1^2` `=` `1` `f(x)` `=` `x-1` 2nd function `f(1)` `=` `1-1` `=` `0` `x=2``f(x)` `=` `x-1` 2nd function `f(2)` `=` `2-1` `=` `1` `x=3``f(x)` `=` `x-1` 2nd function `f(3)` `=` `3-1` `=` `2` `x` `-1` `0` `1` `2` `3` `y` `1` `0` `1,0` `1` `2` Next, plot the points on the graph.Use empty dots for greater than (`>`) values and filled dots for less than or equal (`≤`) values
Finally, form the curve by connecting the points