Question

Function f is shown in the table. What type of function is function f?

Answer 1

Linear Function

Explanation:

A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.

Answer 2

It is an exponential function.

Explanation:

From the given table it is notices than the vale of y is not increasing at the same rate, therefore the function is not linear.

The value of y increases at the increasing rate, therefore the table may be shows the exponential function.

The general for of exponential function is

`y=ab^x`

At x=1, y=2.

`2=ab^1`

`2=ab` .... (1)

At x=-1, y=32.

`32=ab^(-1)`

`32=(a)/(b)` .... (2)

Multiply equation (1) and (2).

`a^2=64`

`a=8`

put this value is equation (1)

`8b=2`

`b=(1)/(4)`

Therefore the function is

`y=8((1)/(4))^x`

Now put all values of x one by one. If all the points satisfied by this equation, then the table shows the exponential function.

At x=-6,

`y=8((1)/(4))^(-6)=8192`

At x=-3,

`y=8((1)/(4))^(-3)=512`

At x=3,

`y=8((1)/(4))^(3)=(1)/(8)`

Since all the points satisfied by this equation, then the table shows the exponential function.