#16 Can you show me how to do this The graph of a linear function f is given.yX1(a) Find the rate of change of f..5(b) Express f in the form f(x) = ax + b.f(x) =.5 + 31.

As we know that the expression for the rate of change of f(x). ∆fx∆x=fx2-fx1x2-x1 From the given…

Answered: The graph of a linear function f is…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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#16 Can you show me how to do this

The graph of a linear function f is given.
y
X
1
(a) Find the rate of change of f.
.5
(b) Express f in the form f(x) = ax + b.
f(x) =
.5 + 3
1.

Expert Solution

Step 1

As we know that the expression for the rate of change of f(x).

$\frac{∆ f (x)}{∆ x} = \frac{f (x_{2}) - f (x_{1})}{x_{2} - x_{1}}$

From the given graph:

(a).

$\begin{array}{rcl} (x_{1}, f (x_{1})) & = & (4, 0) \\ (x_{2}, f (x_{2})) & = & (0, 2) \end{array}$

So,

$\begin{array}{rcl} \frac{∆ f (x)}{∆ x} & = & \frac{f (x_{2}) - f (x_{1})}{x_{2} - x_{1}} \\ = & \frac{2 - 0}{0 - 4} \\ = & - \frac{1}{2} \\ = & - 0.5 \end{array}$

Therefore,

The rate of change of f(x).

$- 0.5$

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The graph of a linear function f is given. y 1 (a) Find the rate of change of f. .5 (b) Express f in the form f(x) = ax + b. %3D f(x) = .5 +3