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)
Step 3: Conclusion
The function g(x)=2x+5 matches all the given g(x) values in the table.