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.
Can u make this in 3 sentences

Answer 1

can u make them short sentences

Answer 2

The function \( f(x) = (x + 2)^2 \) is a quadratic function that produces a parabola opening upwards, with its vertex at the point (-2, 0). In contrast, \( g(x) = 2x + 4 \) is a linear function that produces a straight line with a slope of 2, crossing the y-axis at 4. While both functions are continuous and defined for all real numbers, their shapes differ significantly: one is a curve and the other a straight line, and their rates of change vary, with the quadratic function having a variable slope that increases as \( x \) moves away from the vertex.

Answer 3

The function \( f(x) = (x + 2)^2 \) is a quadratic function that forms an upward-opening parabola with a vertex at (-2, 0). The function \( g(x) = 2x + 4 \) is a linear function that creates a straight line with a slope of 2. While both are continuous, \( f(x) \) has a curved shape, while \( g(x) \) is straight, showing differing rates of change.