Answer
False.
Work Step by Step
False. If they have the same graph then for each value of $a,b$, $f(a+b)=f(a)+f(b)$. But for $a=2,b=3$: $f(a+b)=2^{2+3}=2^5=32\ne12=4+8=2^2+2^3=f(a)+f(b)$
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.