Question

For each table below, could the table represent a function that is linear, exponential, or neither?

Answer 1

f(x) is an exponential function

g(x) is neither linear nor exponential

h(x) is a linear function

Explanation:

The function f(x) we can notice that it is decreasing at a rate that is not constant, but we must calculate the ratio of decrease, if it is constant it is an exponential function:

`\begin{gathered} (80)/(64)=(5)/(4) \\ \\ (64)/(51.2)=(5)/(4) \\ \\ (51.2)/(40.96)=(5)/(4) \end{gathered}`

Which means that f(x) is an exponential function

The function g(x) also decreases non-constantly, we calculate the ratio:

`\begin{gathered} (60)/(24)=(5)/(2) \\ \\ (24)/(-8.8)=-2.72 \end{gathered}`

The ratio is not constant which means that the function g(x) is neither linear nor exponential

The function h(x) decreases constantly, it decreases by 20 per unit, which means that it is a linear function