Step 1
Given :
[tex]f(x)=x^2[/tex]
Required:
[tex]To\text{ shrink by a factor of }\frac{1}{2},\text{ shift 3 units right and 2 units up.}[/tex]
The question did not state clearly if we are to shrink vertically or horizontally. So we will attend to both.
Step 2
A vertical shrink by a factor of 1/2
[tex]\begin{gathered} f(x)=x^2 \\ f(x)\text{ = }\frac{1}{2}x^2 \end{gathered}[/tex]
Step 3
A vertical shrink by a factor of 1/2 and a shift 3 units to the right
[tex]f(x)=\frac{1}{2}(x-3)^2[/tex]
Step 4
A vertical shrink by a factor of 1/2, a shift 3 units to the right, and a shift of 2 units up
[tex]f(x)=\text{ }\frac{1}{2}(x-3)^2+2[/tex]
Step 5
A horizontal shrink by a factor of 1/2
[tex]f(x)\text{ = }2x^2[/tex]
Step 6
A horizontal shrink by a factor of 1/2 and a shift 3 units to the right
[tex]f(x)=2(x-3)^2_{}[/tex]
Step 7
A horizontal shrink by a factor of 1/2, a shift 3 units to the right, and a shift of 2 units up
[tex]f(x)=2(x-3)^2+2[/tex]
Hence the answer will be
If the shrink is vertical by a factor of 1/2, a shift 3 units to the right, and a shift of 2 units up ;
[tex]f(x)=\text{ }\frac{1}{2}(x-3)^2+2[/tex]
If the shrink is horizontal by a factor of 1/2, a shift 3 units to the right, and a shift of 2 units up ;
[tex]f(x)=2(x-3)^2+2[/tex]
