Question

Question #9cf14

Answer 1

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|+k`.

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

`h` is the horizontal shift

`k` is the vertical shift

To graph using transformations, we look at the parent function (in this case `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 `h` value of the transformed function. The y-values of the parent function will first be multiplied be the `a` value of the transformed function, and then modified by adding or subtracting the `k` value.

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

`a` = -1
`h` = -2 (-`h`=+2, so `h`=-2)
`k` = 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]}