Question

You graph the function es002-1.jpg in the standard viewing window of –10 to 10. Will you be able to see the graph? Explain.

Answer 1

I can’t see the file es002-1.jpg here. Please either paste the function rule (e.g. y = f(x)) or describe the picture.

Meanwhile, here is how to decide whether a graph will appear in the standard viewing window (x from −10 to 10, y from −10 to 10):

- Compute (or estimate) the y-values of f(x) for x in [−10,10]. If every y-value is outside the interval [−10,10], the graph will not appear in that window.
- Look for vertical asymptotes inside [−10,10]. Near an asymptote the curve can go to ±∞ and thus be off-screen except possibly short visible pieces.
- Find intercepts and local extrema (use calculus or sampling). If any y-value at an intercept or extremum lies in [−10,10], that part will be visible.
- Also consider resolution: very narrow spikes or very steep features may be effectively invisible or look like a thin line even if they are technically inside the window.

Quick examples:
- y = e^x: on [−10,10] the curve is visible for x ≲ 2.3 (because e^2.3 ≈ 10); for larger x it goes off-screen upward.
- y = 1000x^2: y(±10)=100000, so almost the whole parabola is off-screen except a tiny piece near x = 0.
- y = 1/(x−3)^2: there is a vertical asymptote at x = 3; most of the curve near x = 3 will be off-screen because y→∞, but parts farther from 3 may be visible if y ≤ 10.

If you send the function or the image description I will check it and tell you whether (and which parts of) the graph will be visible.