Question

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

Answer 1

Answer:

It is an exponential function.

Step-by-step 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.

$32=ab^{-1}$

$32=\frac{a}{b}$    .... (2)

Multiply equation (1) and (2).

$a^2=64$

$a=8$

put this value is equation (1)

$8b=2$

$b=\frac{1}{4}$

Therefore the function is

$y=8(\frac{1}{4})^x$

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,

$y=8(\frac{1}{4})^{-6}=8192$

At x=-3,

$y=8(\frac{1}{4})^{-3}=512$

At x=3,

$y=8(\frac{1}{4})^{3}=\frac{1}{8}$

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

Answer 2

Answer:

Linear Function

Step-by-step explanation:

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