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Chapter 3: Q 71. (page 157)

(a) graph each function, (b) determine the domain and the range of the function, and (c) determine where the function is increasing and where it is decreasing.

Hx=-4x2-4x-1

Short Answer

Expert verified

Part (a). The graph is:

Part (b). The domain of the function is all real numbers and the range of the function is (-鈭�,0].

Part (c). The function is increasing in -鈭�,-12and decreasing in -12,鈭�.

Step by step solution

01

Part (a) Step 1. Given information.

The given function isHx=-4x2-4x-1.

02

Part (a) Step 2. Draw the graph.

The required graph is:

03

Part (b) Step 1. Given information.

The given function isHx=-4x2-4x-1.

04

Part (b) Step 2. Determine the domain and range of the given function.

First we draw the graph:

From the above graph, the domain of the function is all real numbers and the range of the function is(-鈭�,0].

05

Part (c) Step 1. Given information.

The given function isHx=-4x2-4x-1.

06

Part (c) Step 2. Determine where the function is decreasing and increasing.

The function is increasing in -鈭�,-12and decreasing in-12,鈭�.

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