Answers:
His first statement is incorrect
His second statement is correct.
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Step-by-step explanation:
The first statement is incorrect because plugging x = 0 into f(x) leads to
f(x) = 3*log(x-7)+1
f(0) = 3*log(0-7)+1
f(0) = 3*log(-7)+1
We stop here because we cannot take the log of a negative number (unless you want a complex number but that's for another time). This means that x = 0 is not in the domain. The domain is x > 7 to ensure that x-7 > 0. That way we avoid taking the log of a negative number, and taking the log of zero as well.
The vertical asymptote is at x = 7 and the log curve is entirely to the right of it, so there's no way it's reaching the y axis.
Simply put: there is no y intercept for this function.
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The second statement is correct.
The function y = log(x) has y go off to infinity when x does.
The same applies to y = 3log(x) and y = 3log(x-7) and y = 3log(x-7)+1
We can say it "rises to the right" as another way of describing part of the end behavior.
A graph can confirm this as shown below.