Q:

# 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

A:
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$$f(x)=ab^x$$From the given table it is noticed that the function passing through the points (1,2) and $$(3,\frac{1}{8})$$. It means the equation must be satisfy by these points.$$2=ab^1$$                  ..... (1)$$\frac{1}{8}=ab^3$$               ..... (2)Divide equation (2) by equation (1).$$\frac{1}{16}=b^2$$$$\frac{1}{4}=b$$Put this value in equation (1).$$2=a\frac{1}{4}$$$$a=8$$The function is$$f(x)=8(\frac{1}{4})^x$$Check the above equation by remaining points.$$f(-5)=8(\frac{1}{4})^{-5}=8\times 1024=8192$$$$f(-3)=8(\frac{1}{4})^{-3}=8\times 64=512$$$$f(-1)=8(\frac{1}{4})^{-1}=8\times 4=32$$Since all the point satisfy the function, therefore the given function is an exponential function. Option 2 is correct.