Q. 79 In Problems 75鈥�80, for the giv... [FREE SOLUTION]

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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 3: Q. 79 (page 157)

In Problems 75鈥�80, for the given functions $f$ and $g,$
(a) Graph $f$ and $g$ on the same Cartesian plane.
(b) Solve $f (x) = g (x) .$
(c) Use the result of part (b) to label the points of intersection of the graphs of $f$ and $g .$
(d) Shade the region for which $f (x) > g (x)$ that is, the region below $f$ and above $g .$
$f (x) = - x^{2} + 5 x; g (x) = x^{2} + 3 x - 4$

Short Answer

Expert verified

(a) The graph of $f$ and $g$ is

(b) $x = 2, 1 .$

(d) The shaded region is

Step by step solution

Part (a) Step 1. Given information

It is given that $f (x) = - x^{2} + 5 x; g (x) = x^{2} + 3 x - 4 .$ We need to draw the graph of $f$ and $g$ in the same cartesian plane.

Step 2. Draw the graph

Part (b) Step 1. Given information

It is given that $f (x) = - x^{2} + 5 x; g (x) = x^{2} + 3 x - 4 .$ We need to solve $f (x) = g (x) .$

Step 2. Solving

$f (x) = g (x) .$

$- x^{2} + 5 x = x^{2} + 3 x - 4 .$

$2 x^{2} - 2 x - 4 = 0 .$

$x^{2} - x - 2 = 0 .$

$x = \frac{1 卤 \sqrt{{(- 1)}^{2} - 4 路 1 路 (- 2)}}{2 路 2} .$

$= \frac{1 卤 \sqrt{1 + 8}}{4} .$

$= \frac{1 卤 \sqrt{9}}{4} .$

$= \frac{1 卤 3}{4} .$

$x = \frac{1 + 3}{2} = 2, a n d x = \frac{1 - 3}{2} = - 1 .$

The values for which $f$ and $g$ are equal, when $x = 2, - 1 .$

Part (c) Step 1. Given information

It is given that $f (x) = - x^{2} + 5 x; g (x) = x^{2} + 3 x - 4 .$ We need to use the result of part (b) to label the point of intersection.

Step 2. Simplify

Let $y = - x^{2} + 5 x = f (x) .$

$y = g (x) = x^{2} + 3 x - 4 .$

When $x = 2, y = - 2^{2} + 5 路 2 = 6 .$

When $x = - 1, y = - {(- 1)}^{2} + 5 路 (- 1) = - 6 .$

The point of intersection is $(2, 6), (- 1, 6) .$

Part (d) Step 1. Given information

It is given that $f (x) = - x^{2} + 5 x; g (x) = x^{2} + 3 x - 4 .$ e need to draw the shaded region for $f (x) > g (x) .$

Step 2. Draw the shaded region

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x	$y = f (x)$
-2	0
-1	1
0	4
1	9
2	16

x	$y = f (x)$
-2	-4
-1	0
0	4
1	8
2	12

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Short Answer

Step by step solution

Part (a) Step 1. Given information

Step 2. Draw the graph

Part (b) Step 1. Given information

Step 2. Solving

Part (c) Step 1. Given information

Step 2. Simplify

Part (d) Step 1. Given information

Step 2. Draw the shaded region

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91影视

In Problems 75鈥�80, for the given functions fand g,(a) Graph fand gon the same Cartesian plane.(b) Solvefx=gx.(c) Use the result of part (b) to label the points of intersection of the graphs of fandg.(d) Shade the region for which fx>gxthat is, the region below fand above g.fx=-x2+5x;gx=x2+3x-4

Short Answer

Step by step solution

Part (a) Step 1. Given information

Step 2. Draw the graph

Part (b) Step 1. Given information

Step 2. Solving

Part (c) Step 1. Given information

Step 2. Simplify

Part (d) Step 1. Given information

Step 2. Draw the shaded region

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Discrete Mathematics

Theoretical and Mathematical Physics

Applied Mathematics

Probability and Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.