Suppose that f (-) = 8200 and f (8) = 2600. (a) Write the linear function f, and (b) find the value of f (5).%3Df(x) = -746.7x+Basic8y

Answered: Suppose that f () = 8200 and f (8) =…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter8: Linear Functions

Section8.7: Function Notation

Problem 2E

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Question

Suppose that f (-) = 8200 and f (8) = 2600. (a) Write the linear function f, and (b) find the value of f (5).
%3D
f(x) = -746.7x+
Basic
8
y

Expert Solution

Step 1

Given

$\begin{array}{l} f (\frac{1}{2}) = 8200 \\ f (8) = 2600 \end{array}$

Step 2

Consider the linear function $f (x)$

$f (x) = a_{0} + a_{1} x ........ (*)$

Now put $x = \frac{1}{2}$ in $(*)$

$\begin{array}{l} 8200 = a_{0} + a_{1} (\frac{1}{2}) \\ 16400 = 2 a_{0} + a_{1} \\ 2 a_{0} + a_{1} = 16400 ........... (1) \end{array}$

$\begin{array}{l} put x = 8 in equation (*) \\ 2600 = a_{0} + a_{1} (8) \\ a_{0} + 8 a_{1} = 2600 ........... (2) \end{array}$

$\begin{array}{l} From equation (1) \\ 2 a_{0} + a_{1} = 16400 \\ a_{1} = 16400 - 2 a_{0} ........ (3) \end{array}$

$\begin{array}{l} a_{0} + 8 a_{1} = 2600 \\ a_{0} + 8 (16400 - 2 a_{0}) = 2600 \\ a_{0} + 131200 - 16 a_{0} = 2600 \\ - 15 a_{0} = 2600 - 131200 \\ - 15 a_{0} = - 128600 \\ a_{0} = \frac{128600}{15} \\ a_{0} = 8573.3 \end{array}$

$\begin{array}{l} Put the value of a_{0} = 8573.3 in equation (3) \\ a_{1} = 16400 - 2 a_{0} \\ a_{1} = 16400 - 2 (8573.3) \\ a_{1} = 16400 - 17146.7 \\ a_{1} = - 746.7 \end{array}$

$\begin{array}{l} f (x) = 8573.3 - 746.7 x \\ f (x) = - 746.7 x + 8573.3 \end{array}$

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