Question #9cf14

1 Answer
Feb 6, 2018

Graph the function using a table of values, making sure to include the vertex.

Explanation:

The general form of an absolute value equation is f(x)=a|x-h|+kf(x)=a|xh|+k.

Where:
aa is the vertical stretch (if |a||a| is > 1) or shrink (if |a||a| is < 1)
If aa is negative, the graph is reflected horizontally.

hh is the horizontal shift

kk is the vertical shift

To graph using transformations, we look at the parent function (in this case f(x)=|x|f(x)=|x| and apply the transformations to the x and y values of the table of values. The x-values of the parent function will be modified by adding or subtracting the hh value of the transformed function. The y-values of the parent function will first be multiplied be the aa value of the transformed function, and then modified by adding or subtracting the kk value.

In the example provided above, H(x)=-|x+2|H(x)=|x+2| so:

aa = -1
hh = -2 (-hh=+2, so hh=-2)
kk = 0

The table of values for the parent function looks like this:

X | Y


-2 | 2
-1 | 1
0 | 0
1 | 1
2 | 2

The transformed table of values would look like this:

X + h | aY + k


-2-2=-4 | -1(2)+0=-2
-1-2=-3 | -1(1)+0=-1
0-2=-2 | -1(0)+0=0
1-2=-1 | -1(1)+0=-1
2-2=0 | -1(2)+0=-2

(Sorry about the table format...)
graph{-|x+2| [-10, 10, -5, 5]}