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What is the range of the function fx=4x212?

Aallintegerslessthanorequalto12B{allnonnegativeintegers}C{allrealnumbers}D{allrealnumberslessthanorequalto}

Short Answer

Expert verified

The range of the given function is all real numbers less than or equal to 12.

Step by step solution

01

Step 1. Identify.

The functionfx=4x212 is a parabola witha=4,b=0 and c=12. As a is negative, the graph opens downward, and the function has a maximum value. The range is all real numbers less than or equal to the maximum value.

02

Step 2. Find x coordinate of vertex.

X coordinate of vertex is given by x=b2a. Substitute -4 for a, 0 for b and 12 for c

x=024=0

03

Step 3. Find the value of y.

Substitute x-coordinate of vertex into the original equation,

fx=4x212=40212=12

Therefore, the vertex is at 0,12.

The maximum value is 12. The range is all real numbers less than or equal to the maximum value, or all real numbers less than or equal to 12. Option D is the required answer.

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