Q:

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

Accepted Solution

A:
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.