Chapter Test
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Write g(x) in terms of f(x). Apply one transformation at a time.
Transformations: The transformations are a reflection in the x-axis, then a vertical translation 3 units up.
We are asked to graph f(x)=x and g(x)=- x+3. Also, we need to find the transformations from the graph of f to the graph of g.
To graph f(x), we will first make a table of values.
| x | f(x) |
|---|---|
| -3 | -3 |
| 0 | 0 |
| 3 | 3 |
Before graphing, let's rewrite g(x) it in terms of f(x). g(x)=- x+3 ⇒ g(x)=- f(x)+3 Note that the first part of the function is - f(x), which means that the parent function f(x)=x is reflected in the x-axis.
Now, we can see that the second term of g(x) is + 3, which means a vertical translation 3 units up from the graph of - f(x).
Therefore, we can see that the graph of g(x)=- x+3 is a reflection in the x-axis, then a vertical translation 3 units up from the graph of f.
