Questions: Which of the following functions represents (g(x)) ? (x) (g(x)) -3 -1 -2 1 -1 3 0 5 1 7 2 9 (g(x)=x+2) (g(x)=2x+5) (g(x)=3x+2) (g(x)=2x+1)

Transcript text: Which of the following functions represents $g(x)$ ? \begin{tabular}{|c|c|} \hline $\mathbf{x}$ & $\mathbf{g}(\mathbf{x})$ \\ \hline-3 & -1 \\ \hline-2 & 1 \\ \hline-1 & 3 \\ \hline 0 & 5 \\ \hline 1 & 7 \\ \hline 2 & 9 \\ \hline \end{tabular} $g(x)=x+2$ $g(x)=2 x+5$ $g(x)=3 x+2$ $g(x)=2 x+1$

Solution

Solution Steps

To determine which function represents $ g(x) $, we need to check which of the given function options fits the data in the table for $ g(x) $. We will evaluate each function at the given $ x $ values and see which one matches the corresponding $ g(x) $ values.

Step 1: Identify the Functions

We are given four candidate functions for $ g(x) $:

$ g(x) = x + 2 $
$ g(x) = 2x + 5 $
$ g(x) = 3x + 2 $
$ g(x) = 2x + 1 $

Step 2: Evaluate Each Function

We will evaluate each function at the specified $ x $ values from the table and compare the results with the corresponding $ g(x) $ values:

For $ g(x) = x + 2 $:
- $ g(-3) = -3 + 2 = -1 $
- $ g(-2) = -2 + 2 = 0 $ (does not match)
For $ g(x) = 2x + 5 $:
- $ g(-3) = 2(-3) + 5 = -6 + 5 = -1 $
- $ g(-2) = 2(-2) + 5 = -4 + 5 = 1 $
- $ g(-1) = 2(-1) + 5 = -2 + 5 = 3 $
- $ g(0) = 2(0) + 5 = 0 + 5 = 5 $
- $ g(1) = 2(1) + 5 = 2 + 5 = 7 $
- $ g(2) = 2(2) + 5 = 4 + 5 = 9 $ (matches all)
For $ g(x) = 3x + 2 $:
- $ g(-3) = 3(-3) + 2 = -9 + 2 = -7 $ (does not match)
For $ g(x) = 2x + 1 $:
- $ g(-3) = 2(-3) + 1 = -6 + 1 = -5 $ (does not match)