QuestionFind the equation for the function $f(x)$ using these points: (2, 4.6), (4, 6.0), (6, 7.4), (8, 8.8), (10, 10.2).

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is linear, as the difference between consecutive $f(x)$ values is constant. . The data points provided are accurate and no outliers are present.

STEP 2

First, we need to find the slope of the function. The slope of a linear function is the change in $f(x)$ divided by the change in $x$ . We can calculate it using the formula $slope = \frac{f(x2) - f(x1)}{x2 - x1}$

STEP 3

Now, plug in the values for $f(x2)$ , $f(x1)$ , $x2$ , and $x1$ from the first two data points to calculate the slope.
$slope = \frac{6.0 -.6}{ -2}$

STEP 4

Calculate the slope.
$slope = \frac{6.0 -4.6}{4 -2} =0.7$

STEP 5

Now that we have the slope, we can find the y-intercept (b) of the function. The y-intercept is the value of $f(x)$ when $x =0$ . We can calculate it using the formula $b = f(x) - slope \cdot x$

STEP 6

Plug in the values for $f(x)$ , $slope$ , and $x$ from any of the data points to calculate the y-intercept.
$b =4.6 -0. \cdot2$

STEP 7

Calculate the y-intercept.
$b =4.6 -0.7 \cdot2 =3.2$

STEP 8

Now that we have the slope and the y-intercept, we can write the equation that represents the function $f(x)$ .
$f(x) = slope \cdot x + b$

STEP 9

Plug in the values for the slope and the y-intercept to write the equation.
$f(x) =.7x +3.2$ The equation that represents the function $f(x)$ is $f(x) =.7x +3.2$ .

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms