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Chapter 9: Q77. (page 535)

What is the range of the function fx=鈭�4x2鈭�12?

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

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Identify.

The functionfx=鈭�4x2鈭�12 is a parabola witha=鈭�4,b=0 and c=鈭�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=鈭�b2a. Substitute -4 for a, 0 for b and 鈭�12 for c

x=鈭�02鈭�4=0

03

Step 3. Find the value of y.

Substitute x-coordinate of vertex into the original equation,

fx=鈭�4x2鈭�12=鈭�402鈭�12=鈭�12

Therefore, the vertex is at 0,鈭�12.

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

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Most popular questions from this chapter

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1000,鈥夆赌�500鈥夆赌�,鈥夆赌�250鈥夆赌�.....

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