Question

Write a linear function f with f(2)=−2 and f(1)=1.

Answer 1

Answer - the answer should be: -3x+4

down below is how i did it,

Step-by-step explanation:

use the formula mx+b=y

y is f(x)

m = -3

x = x

b = 4

so,

mx+b is -3x+4

Answer 2

A linear function is the function of a straight line.

The linear function is: $\mathbf{f(x) = -3x + 4}$

The given parameters are:

$\mathbf{f(2) =-2}$

$\mathbf{f(1) =1}$

Calculate the slope (m)

$\mathbf{m = \frac{f(b) - f(a)}{b -a}}$

So, we have:

$\mathbf{m = \frac{-2-1}{2 -1}}$

$\mathbf{m = \frac{-3}{1}}$

$\mathbf{m = -3}$

The linear function is then calculated as:

$\mathbf{y = m(x - x_1) + y_1}$

This gives

$\mathbf{y = -3(x - 1) + 1}$

$\mathbf{y = -3x + 3 + 1}$

$\mathbf{y = -3x + 4}$

Rewrite as:

$\mathbf{f(x) = -3x + 4}$

Hence, the linear function is: $\mathbf{f(x) = -3x + 4}$

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