Function f is shown in the table.What type of function is function f?linearexponentialneither linear nor exponentialThe table is:x f(x)−5 8192−3 512−1 321 23 18
Accepted Solution
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Answer:The correct option is 2. The given function is an exponential function.Step-by-step explanation:From the given table it is noticed that the rate of change is not constant, therefore it is not a linear function.The general form of an exponential function is[tex]f(x)=ab^x[/tex]From the given table it is noticed that the function passing through the points (1,2) and [tex](3,\frac{1}{8})[/tex]. It means the equation must be satisfy by these points.[tex]2=ab^1[/tex] ..... (1)[tex]\frac{1}{8}=ab^3[/tex] ..... (2)Divide equation (2) by equation (1).[tex]\frac{1}{16}=b^2[/tex][tex]\frac{1}{4}=b[/tex]Put this value in equation (1).[tex]2=a\frac{1}{4}[/tex][tex]a=8[/tex]The function is[tex]f(x)=8(\frac{1}{4})^x[/tex]Check the above equation by remaining points.[tex]f(-5)=8(\frac{1}{4})^{-5}=8\times 1024=8192[/tex][tex]f(-3)=8(\frac{1}{4})^{-3}=8\times 64=512[/tex][tex]f(-1)=8(\frac{1}{4})^{-1}=8\times 4=32[/tex]Since all the point satisfy the function, therefore the given function is an exponential function. Option 2 is correct.