Extrapolation

Extrapolation is defined by where the explanatory value sits, not by how the answer looks. If the $x$ you substitute falls outside the interval of $x$-values used to fit the line, the prediction is an extrapolation even when it comes out perfectly plausible, and an $x$ inside that interval is not an extrapolation even when the prediction turns out badly. The range of the response has nothing to do with it.

Six students study 1, 2, 3, 4, 5 and 6 hours and score 60, 72, 65, 78, 71 and 86, giving $\hat{y} = 58 + 4x$. Predict for a student who studies 12 hours and the line returns $58 + 4(12) = 106$ on a test scored out of 100. The arithmetic is correct. What is missing is any observation past 6 hours, so nothing in these data says the gain of 4 points per hour keeps going rather than flattening off, and the line has no way to know that scores stop at 100.

The defense to reject is "the fit is strong, so the prediction is fine." Strength is measured over the observed range only. Here $r = 0.8107$ and $r^2 = 0.657$ describe how the line does between 1 and 6 hours, and both are unchanged by which $x$ you feed the equation afterwards. Regression output prints no warning when you leave the data behind, so the check has to be yours: write down the smallest and largest $x$ before predicting.

Extrapolation is not banned. Forecasting is often the whole point of fitting a line, and a prediction just past the edge of the data is usually more defensible than one far beyond it. What you lose is the ability to check the assumption against evidence, so an extrapolated value gets stated with its assumption attached. The y-intercept is the case people miss: $a = 58$ is the predicted score at $x = 0$ hours, which is outside the range 1 to 6, so reading it as a claim about a student who does not study at all is itself an extrapolation.