Chapter Test
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Make a table of values to find points on the graph. Think about the horizontal transformations before thinking about any vertical transformations. Work from the inside
to the outside.
Graph:
Transformations:
Horizontal translation 2 units to the left.
Horizontal shrink by a factor of 12.
First, we will make a table of values to graph these functions. After that, we will go through all the transformations from the graph of f(x)=|x| to the graph of g(x)=|2x+4|.
Let's make a table of values for each of the functions. After that, we will plot the ordered pairs that we find and connect them. Let's start with f(x).
| x | |x| | f(x) |
|---|---|---|
| -4 | | -4| | 4 |
| -2 | | -2| | 2 |
| 0 | | 0| | 0 |
| 2 | | 2| | 2 |
| 4 | | 4| | 4 |
| x | |2x+4| | g(x) |
|---|---|---|
| -4 | |2( -4)+4| | 4 |
| -3 | |2( -3)+4| | 2 |
| -2 | |2( -2)+4| | 0 |
| -1 | |2( -1)+4| | 2 |
| 0 | |2( 0)+4| | 4 |
Let's plot the points of each function and connect them. We will do this in the same coordinate plane.
We wil look at each of the transformations individually and work our way from the inside
to the outside.
g(x)=|2x+4|
The given equation is a transformation of the parent function f(x)=|x|. To see how each of the parameters is affecting the parent function, it will be helpful to rewrite it first.
g(x)&=|2x+4|
&⇕
g(x)&=|2(x+2)|
We will start with the transformation closest to x and end with the farthest from x. First, there is a horizontal translation 2 units to the left.
|x|⇒|x+ 2|
Remember, typically |x-h| is a horizontal translation h units to the right, while |x+h| is translated h units to the left.
Next, we have a horizontal shrink by a factor of 12. This transforms the graph of y=|x+2| to the graph of y=|2x+4|.
