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)

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

Solution

failed
failed

Solution Steps

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

Step 1: Identify the Functions

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

  1. g(x)=x+2 g(x) = x + 2
  2. g(x)=2x+5 g(x) = 2x + 5
  3. g(x)=3x+2 g(x) = 3x + 2
  4. g(x)=2x+1 g(x) = 2x + 1
Step 2: Evaluate Each Function

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

  • For g(x)=x+2 g(x) = x + 2 :

    • g(3)=3+2=1 g(-3) = -3 + 2 = -1
    • g(2)=2+2=0 g(-2) = -2 + 2 = 0 (does not match)
  • For g(x)=2x+5 g(x) = 2x + 5 :

    • g(3)=2(3)+5=6+5=1 g(-3) = 2(-3) + 5 = -6 + 5 = -1
    • g(2)=2(2)+5=4+5=1 g(-2) = 2(-2) + 5 = -4 + 5 = 1
    • g(1)=2(1)+5=2+5=3 g(-1) = 2(-1) + 5 = -2 + 5 = 3
    • g(0)=2(0)+5=0+5=5 g(0) = 2(0) + 5 = 0 + 5 = 5
    • g(1)=2(1)+5=2+5=7 g(1) = 2(1) + 5 = 2 + 5 = 7
    • g(2)=2(2)+5=4+5=9 g(2) = 2(2) + 5 = 4 + 5 = 9 (matches all)
  • For g(x)=3x+2 g(x) = 3x + 2 :

    • g(3)=3(3)+2=9+2=7 g(-3) = 3(-3) + 2 = -9 + 2 = -7 (does not match)
  • For g(x)=2x+1 g(x) = 2x + 1 :

    • g(3)=2(3)+1=6+1=5 g(-3) = 2(-3) + 1 = -6 + 1 = -5 (does not match)
Step 3: Conclusion

The function g(x)=2x+5 g(x) = 2x + 5 matches all the given g(x) g(x) values in the table.

Final Answer

The answer is g(x)=2x+5 \boxed{g(x) = 2x + 5} .

Was this solution helpful?
failed
Unhelpful
failed
Helpful