Function Question

Question

The function whose values are given in the table below is ether linear or exponential. Find a formula for this function. 

x    F(x)

0     310

1     324

2     338

3     352

Answer 1

You are told this is either linear of exponential

 

Check to see: 

 

Do you add the same number to each y-value to 

get the next y-value........linear

 

Or, do you multiply each y-value by  the same

number to get the next y-value......exponential

 

In your problem 14 is added to y in order to get 

the next y value, you have a linear function:

 

       F(X) = mX + b

 

you must replace m and b with numbers

 

where: m is the number being added to each y-value

           to get the next y-value:   14

 

           b is the y-value when x = 0; according to 

           your chart  y = 310  when x = 0

 

Therefor your equation is:  F(X) = 14X + 310

Answer 2

The numbers are changing at a constant rate so the Eq. will be linear and can be written using the basic Eq. of a line:

 

y = mx + b

 

b is the y-intercept (what y equals when x =0) so..  310

 

m is the slope, or rate of change.

 

choose any two points (x₁, y₁) and (x₂, y₂) in your table;

 

then use m = (y₁ - y₂) / (x₁ - x₂)

 

 

Answer 3

In a linear function the output - f(x) - changes at a constant rate.

For the numbers given, do the f(x) values change by the same amount?