Rule for g : g(x)= - x^4 +3x^2 +2x Transformation: Reflection in the x-axis.
Practice makes perfect
We will describe the graph of g as a transformation of the graph of f. Then we will write a rule for g.
Describing the Transformation
To describe and graph the given transformation, g(x)=- f(x), let's look at the possible transformations. Then we can more clearly identify the ones being applied to the function f(x)=x^4-3x^2-2x.
Reflections
In the x-axis
y= - f(x)
In the y-axis
y=f( - x)
Now, using the table, let's highlight the transformations of f(x).
g(x)= - f(x)
Therefore, the graph of g is a reflection in the x-axis of the graph of f.
Finding the Rule for g(x)
Let's write the rule for - f(x).
- f(x)=- (x^4-3x^2-2x) ⇕
- f(x)= - x^4 +3x^2 +2x
Finally, we have the rule for g(x).
g(x)= - x^4 +3x^2 +2x
