Chapter 3: Q 68. (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.
$G (x) = 3 x^{2} + 2 x + 5$

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 $[4.66, + \infty)$ .

Part (c). The function is increasing in $(- 0.33, \infty)$ and decreasing in $(- \infty, - 0.33)$ .

Step by step solution

Part (a) Step 1. Given information.

The given function is $G (x) = 3 x^{2} + 2 x + 5$ .

Part (a) Step 2. Draw the graph.

Part (b) Step 1. Given information.

The given function is $G (x) = 3 x^{2} + 2 x + 5$ .

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

From the above graph the domain of the given function is all real numbers and the range of the function is $[4.66, \infty)$ .

Part (c) Step 1. Given information.

The given function is $G (x) = 3 x^{2} + 2 x + 5$ .

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

The function is increasing in $(- 0.33, \infty)$ and decreasing in $(- \infty, - 0.33)$ .

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x	$y = f (x)$
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0	0
1	1
2	0

(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.
$G (x) = 3 x^{2} + 2 x + 5$

Short Answer

Step by step solution

Part (a) Step 1. Given information.

Part (a) Step 2. Draw the graph.

Part (b) Step 1. Given information.

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

Part (c) Step 1. Given information.

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

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(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.Gx=3x2+2x+5

Short Answer

Step by step solution

Part (a) Step 1. Given information.

Part (a) Step 2. Draw the graph.

Part (b) Step 1. Given information.

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

Part (c) Step 1. Given information.

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Mechanics Maths

Discrete Mathematics

Logic and Functions

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

(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.
$G (x) = 3 x^{2} + 2 x + 5$