Rule for g: g(x)=3x^5-6x+9 Transformation: Vertical stretch by a factor of 3. Graph:
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. Finally, we will graph the functions.
Describing the Transformation
To describe and graph the given transformation, g(x)=3f(x), let's look at the possible transformations. Then we can more clearly identify the ones being applied to the function f(x)=x^5-2x+3.
Vertical Stretch or Shrink
Vertical stretch, a>1
y= af(x)
Vertical shrink, 0< a< 1
y= af(x)
Now, using the table, let's highlight the transformations of f(x).
g(x)= 3f(x)
We can describe the transformation as a vertical stretch by a factor of 3.
Finding the Rule for g(x)
To obtain the rule for g(x), we will write the rule for 3f(x). To do so, we will multiply the formula of f(x) by 3.
f(x)=x^5-2x+3 ⇒ 3f(x)= 3(x^5-2x+3)
Let's now simplify the above formula.
