Question

Juan recently entered into a contract for a cell phone plan. The table shows the monthly cost in dollars, f(x), if Juan sends x text messages.



What type of function is represented?

linear
quadratic
logarithmic
exponential

Answer 1

I don't see the table of values — could you paste it? With the numbers I can tell you exactly.

Meanwhile, here is how you can determine the type from a table:

- Compute the first differences: Δf = f(x+1) − f(x).
- If the first differences are constant for equal steps in x, the function is linear.

- If first differences are not constant, compute the second differences: Δ²f = Δf(x+1) − Δf(x).
- If the second differences are constant, the function is quadratic.

- If neither differences are constant, compute successive ratios r = f(x+1)/f(x).
- If the ratios are (approximately) constant, the function is exponential.

- Logarithmic growth shows rapidly increasing first differences at small x that slow as x grows; it will not have constant differences or constant ratios.

Also, for a cell‑phone plan the cost is commonly a fixed monthly fee plus a fixed per‑text charge, which produces a linear function (f(x) = base + rate·x). If you post the table I’ll apply these tests and give the definite answer.