Question

use transformations of f(x)=x² to graph the following function. g(x)=x²+5 answer below. a. the graph of f(x)=x² should be shifted 5 units to the right. b. the graph of f(x)=x² should be shifted 5 units to the left. c. the graph of f(x)=x² should be shifted 5 units up. d. the graph of f(x)=x² should be shifted 5 units down. use the graphing tool to graph the function. click to enlarge graph

Explanation:

For a parent function $f(x) = x^2$, a transformation of the form $g(x) = f(x) + k$ results in a vertical shift. When $k>0$, the graph shifts upward by $k$ units. Here, $k=5$, so the graph of $f(x)=x^2$ shifts 5 units up.

Answer:

C. The graph of $f(x)=x^2$ should be shifted 5 units up.