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ACT® Math

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Moderate

Comparing Functions

ACTMAT-4KKVOK

The figure below is of the graphs of:

$$ f(x) = -\frac{1}{4}(x-\frac{1}{2})^2 + \frac{49}{16} $$

...and:

$$ g(x) = \frac{1}{2}x^{2}-2x $$

...in the x-y coordinate plane.

For which of the following intervals for $x$ is $g(x) < f(x) $?

A

$ -3<$ $x$ $<4 $

B

$ -1<$ $x$ $<4 $

C

$ 0<$ $x$ $<4 $

D

$ x<-3$ and $x>4 $

E

$ x<-1$ and $x>4 $