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.

Answer 1

f(x) = (x+2)^2 is a U-shaped parabola opening upward with vertex at (-2, 0), axis of symmetry x = -2, domain all real numbers and range y ≥ 0; its y-intercept is f(0) = 4 and it has a double x-intercept at (-2,0). g(x) = 2x + 4 is a straight line with slope 2, y-intercept (0,4), x-intercept (-2,0), and domain and range all real numbers. The two graphs meet at two points, (-2,0) and (0,4). They are similar in that they share those points and the same y-value at x = 0, but they differ in shape and behavior: f is a nonlinear parabola with a minimum and symmetry, while g is a linear function with constant slope and no minimum.