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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 2: Q. 65 (page 91)

$f (x) = 5 x - 2$
(a) Find the average rate of change from $1$ to $3 .$
(b) Find the equation of the secant line containing $(1, f (1))$ and $(3, f (3))$ .

Short Answer

Expert verified

(a) The average rate of change is $5 .$

(b) The equation of the secant line isrole="math" localid="1646224686021" $y = 5 x - 8$ .

Step by step solution

01

Step 1. Given information.

We have:

$f (x) = 5 x - 2$

02

Part a. Step 1. Find the average rate of change from 1 to 3.

The equation is $f (x) = 5 x - 2$ .

Average rate of change is given by:

localid="1646229963744" $\frac{鈭� y}{鈭� x} = \frac{f (b) - f (a)}{b - a}$

Here, $a = 1, b = 3$

$\frac{鈭� y}{鈭� x} = \frac{f (3) - f (1)}{3 - 1} = \frac{5 (3) - 2 - (5 (1) - 2)}{2} = 5$

03

Part b. Step 1. Find the equation of the secant line.

The equation is $f (x) = 5 x - 2$ and the point $(2, f (2))$ , $(3, f (3))$ .

Substitute $x = 2$ in the equation:

$f (2) = 5 (2) - 2 = 10 - 2 = 8$

The slope of the secant line is equal to the average rate of change of a function, it follows:

$m_{\sec} = 5$

Therefore, use the point-slope form to equation of the secant line:

localid="1646230369239" $y - y_{1} = m_{\sec} (x - x_{1}) y - 2 = 5 (x - 2) y = 5 x - 10 + 2 y = 5 x - 8$

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Most popular questions from this chapter

Suppose that the graph of a function $g$ is known. The graph of $y = g (x) + 2$ may be obtained by a _______ shift of the graph of $g$ ________ a distance of $2$ units.

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