Question

what is the function g(x) created from f(x)=x² by moving the graph right 3 units, adding vertical compression by a factor of 1/2, and shifting the graph down 5 units? a g(x)=3(x+5)²+1/2 b g(x)=5(x-3)²+1/2 c g(x)=1/2(x+3)²+5 d g(x)=1/2(x-3)²-5

Explanation:

Step1: Horizontal shift right 3 units

$h(x) = (x-3)^2$

Step2: Vertical compression by $\frac{1}{2}$

$k(x) = \frac{1}{2}(x-3)^2$

Step3: Vertical shift down 5 units

$g(x) = \frac{1}{2}(x-3)^2 - 5$

Answer:

D. $g(x)=\frac{1}{2}(x-3)^2 - 5$