Answer:
Option 3: The graph of g(x) has a vertical shrink by a factor of 1/2 and a vertical shift up by 5 units from the function of f(x).
Explanation:
Given the function f(x) where:
[tex]f(x)=x^3-2[/tex]
We want to determine the transformations applied on f(x) so that it falls onto g(x) where:
[tex]g(x)=\frac{1}{2}x^3+3[/tex]
Step 1: Since the product of x³ i.e. 1/2 is less than one, f(x) has been vertically shrunk by a factor of 1/2 to obtain:
[tex]\frac{1}{2}x^3-2[/tex]
Step 2: If the result is vertically shifted up by 5 units, then:
[tex]\frac{1}{2}x^3-2+5=\frac{1}{2}x^3+3=g(x)[/tex]
Thus, the graph of g(x) has a vertical shrink by a factor of 1/2 and a vertical shift up by 5 units from the function of f(x).
The third option is correct.
