We will describe the graph of g as a transformation of the graph of f. Then we will write a rule for g. Finally, we will graph the functions.
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^5-4x+6.
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)
We can describe the transformations as a reflection in the x-axis.
Finding the Rule for g(x)
To find the rule for g(x), let's write the rule for - f(x).
f(x)=x^5-4x+6 ⇒ - f(x)= -( x^5-4x+6)
Let's now simplify the above formula.
