Q. 26 - Precalculus Enhanced with Graphing Utilities

Question

determine whether the given function is linear, exponential, or neither. For those that are linear functions, find a linear

function that models the data; for those that are exponential, find an exponential function that models the data.

x	f(x)
-1	2
0	5
1	8
2	11
3	14

Step-by-Step Solution

Answer

The function is linear whose equation is 

$g\left(x\right)=3x+5$

Step 1. Given

A table with values of $x,f\left(x\right)$to trace the function.

Step 2. Write the concept

We will check for domain and range that will gives us a clue about exponentiality or linearity of the function.

Step 3. Calculation

Here the change in domain is just 1 unit but change in range is of higher order.

Also the change is constant therefore, it is linear.

Consider,

$$\begin{gathered} g\left(x\right)=mx+c \\ at x=0 we have g\left(x\right)=5 \\ therefore, \\ c=5 \\ Now at x=-1 g\left(x\right)=2 \\ therefore, \\ 2=m(-1)+5 \\ m=3 \\ thus, g\left(x\right)=3x+5 \end{gathered}$$