#1**+1 **

This is an example of a piecewise function.

\(\begin{array}{cc} \{ & \begin{array}{cc} 0 &\text{if}& x\leq -3 \\ x+1 &\text{if}& -2

Unfortunately, I am not an expert with LaTeX, so I do not know how to enlarge the bracket to the appropriate size. Maybe someone is more adept.

Anyway, the best advice I can give for problems like these is to do them one step at a time. Let's worry about the topmost function and work our way downward.

\(-1\hspace{1mm}\text{if}\hspace{1mm}x\leq3\)

If y=-1, that means that no matter what the input is, the output will always be -1. Therefore, plot this such that y=-1. However, we must be mindful of the domain restriction. This is only true when the input (x) is less than or equal to 3. 4, for example, does not exist because that input is outside of the domain restriction. Be sure to have a closed circle at (3,-1) to indicate that that value is included. Now, let's worry about the next piece!

\(x+1\hspace{1mm}\text{if}\hspace{1mm} -2

Plot the function \(y=x+1\) just like you normally would. Just like before, we then take into account the currect restriction. Be sure to have an open circle at the point \((-2,-1)\) because it is not included, and be sure to have a closed circle at \((2,3)\) because that point is included according to the domain restriction.

\(x\hspace{1mm}\text{if}\hspace{1mm}4\leq x\leq6\)

Plot the function as if the equation was \(y=x\). Then, chop off the points where x and then only include the domain values bounded between 4 and 6. Be sure to have closed circles.

Click anywhere on this sentence to be sent to a graph of this specific peicewise function.

TheXSquaredFactor
Oct 4, 2017

#1**+1 **

Best Answer

This is an example of a piecewise function.

\(\begin{array}{cc} \{ & \begin{array}{cc} 0 &\text{if}& x\leq -3 \\ x+1 &\text{if}& -2

Unfortunately, I am not an expert with LaTeX, so I do not know how to enlarge the bracket to the appropriate size. Maybe someone is more adept.

Anyway, the best advice I can give for problems like these is to do them one step at a time. Let's worry about the topmost function and work our way downward.

\(-1\hspace{1mm}\text{if}\hspace{1mm}x\leq3\)

If y=-1, that means that no matter what the input is, the output will always be -1. Therefore, plot this such that y=-1. However, we must be mindful of the domain restriction. This is only true when the input (x) is less than or equal to 3. 4, for example, does not exist because that input is outside of the domain restriction. Be sure to have a closed circle at (3,-1) to indicate that that value is included. Now, let's worry about the next piece!

\(x+1\hspace{1mm}\text{if}\hspace{1mm} -2

Plot the function \(y=x+1\) just like you normally would. Just like before, we then take into account the currect restriction. Be sure to have an open circle at the point \((-2,-1)\) because it is not included, and be sure to have a closed circle at \((2,3)\) because that point is included according to the domain restriction.

\(x\hspace{1mm}\text{if}\hspace{1mm}4\leq x\leq6\)

Plot the function as if the equation was \(y=x\). Then, chop off the points where x and then only include the domain values bounded between 4 and 6. Be sure to have closed circles.

Click anywhere on this sentence to be sent to a graph of this specific peicewise function.

TheXSquaredFactor
Oct 4, 2017