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[tex]y=ab^x[/tex]At x=1, y=2.[tex]2=ab^1[/tex][tex]2=ab[/tex] .... (1)At x=-1, y=32.[tex]32=ab^{-1}[/tex][tex]32=\frac{a}{b}[/tex] .... (2)Multiply equation (1) and (2).[tex]a^2=64[/tex][tex]a=8[/tex]put this value is equation (1)[tex]8b=2[/tex][tex]b=\frac{1}{4}[/tex]Therefore the function is [tex]y=8(\frac{1}{4})^x[/tex]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,[tex]y=8(\frac{1}{4})^{-6}=8192[/tex]At x=-3,[tex]y=8(\frac{1}{4})^{-3}=512[/tex]At x=3,[tex]y=8(\frac{1}{4})^{3}=\frac{1}{8}[/tex]Since all the points satisfied by this equation, then the table shows the exponential function.