Question

How do you graph absolute value equations on a coordinate plane?

Answer 1

Hint:
Absolute value equations are the equations in which the absolute value operator is used. To graph such an equation, we must first get rid of the absolute value equation by dividing the equation into different parts. Then graph the equations of these parts separately.

Complete step by step solution:
Let us first understand what absolute value equations.
Absolute value equations are the equations in which the absolute value operator is used. An absolute value operator is an operator which gives us only the positive (or absolute) value of the expression in the operator.
This means if the value of the expression or the number inside the operator is positive, then the result is the same expression or the same number.
If the value of the expression or the number inside the operator is negative, then the result is the negative of the expression or the number.
Suppose we have an expression $|x+1|$.
Then if (x+1) is positive or equal to 0, then $|x+1|=x+1$
However, is (x+1) is negative, then $|x+1|=-(x+1)=-x-1$.
To graph such an equation, we must first get rid of the absolute value equation by dividing the equation into different parts. Then graph the equations of these parts separately.
Consider $y=|x+1|$
We know that if $x+1\ge 0$, then $|x+1|=x+1$
This means that if $x\ge -1$, then $|x+1|=x+1$
Which means that $y=x+1$ for $x\ge -1$
Draw the graph for $y=x+1$ where $x\ge -1$.
Similarly, we know that if $x+1<0$, then $|x+1|=-x-1$
This means that if $x<-1$, then $|x+1|=-x-1$
This further means that $y=-x-1$ for $x<-1$
Draw the graph for $y=x+1$ where $x\ge -1$.

Note:
For continuous functions that is a shortcut.
Suppose we have $y=|f(x)|$.
To plot the graph of the above function, first draw the graph for $y=f(x)$, then flip the curve about the x axis where the value of y is negative, since we can only have a positive value of y.