Comparing Exponential, Linear, and Quadratic Growth — Quiz
Question 7 • Algebra I
For which pair of functions is the exponential consistently growing at a faster rate than the quadratic over the interval 0 is less than or equal to x comma x is less than or equal to 5 ?
Answer
A
Image with description On a coordinate plane, the x axis lists negative 1 to 5 by 1, and the y axis lists negative 2 to 8 by 1. The graph has two smooth curves. The first smooth curve originates below the negative direction of the x axis, goes through (0 comma 0), and moves further up. The second smooth curve is a parabola that opens up and has a vertex at the origin. It goes through (1 comma 3) and moves up. Both curves touch each other at the origin.
B
Image with description On a coordinate plane, the x axis lists negative 1 to 5 by 1 unit. The y axis lists negative 2 to 8 by 1 unit. The parabola opens up, has vertex at the origin, and passes through (negative 1 comma 4) and (1 comma 4). The curve goes through (0 comma 1), (1 comma 2), (2 comma 4), and (3 comma 8).
C
Image with description On a coordinate plane, the x axis lists negative 1 to 5 by 1, and the y axis lists negative 2 to 8 by 1. The graph has two smooth curves. The first smooth curve originates from the negative direction of the x axis, intersects the y axis at (0 comma 1), goes through (1 comma 4), and moves up. The second smooth curve is a parabola that opens up and has a vertex at the origin. It goes through (2, 2) and moves up.
D
Image with description On a coordinate plane, the x axis lists negative 1 to 5 by 1 unit. The y axis lists negative 2 to 8 by 1 unit. The parabola opens up, has vertex at the origin, and passes through (negative 1 comma 2) and (1 comma 2). The curve goes through (0 comma 1), (1 comma 2), (2 comma 4), and (3 comma 8).