Question

Graph and compare the shapes and key features of the functions f(x)=(x+2)2
and g(x)=2x+4
. In 3–5 sentences, explain how the two functions are similar and how they are different.(4 points)

Answer 1

f(x) = (x+2)^2 is a parabola opening upward with vertex at (-2, 0), axis of symmetry x = -2, y-intercept f(0) = 4, domain all real numbers and range y ≥ 0. g(x) = 2x + 4 is a straight line with slope 2, y-intercept 4 and x-intercept -2, domain and range all real numbers. The two graphs intersect at the two points (-2, 0) and (0, 4), so they share those intercepts and both are defined for all x. They differ in shape and behavior: f is curved with a single minimum and changing slope, while g is linear with constant slope and no extrema.