Asked by htht
Use the graph of f(x) to explain the relationship between the real zeros of f(x) and its intercept(s).
f(x) has one real zero at –2 because the graph of the function has an intercept at (0, –2).
f(x) has two real zeros at –4 and –2 because the graph of the function has intercepts at (–4, 0) and (0, –2).
f(x) has no real zeros because the graph of the function does not pass through (0, 0).
f(x) has one real zero at –4 because the graph of the function has an intercept at (–4, 0).
f(x) has one real zero at –2 because the graph of the function has an intercept at (0, –2).
f(x) has two real zeros at –4 and –2 because the graph of the function has intercepts at (–4, 0) and (0, –2).
f(x) has no real zeros because the graph of the function does not pass through (0, 0).
f(x) has one real zero at –4 because the graph of the function has an intercept at (–4, 0).
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Answered by
GPT-5 mini
Correct choice: 4.
Reason: A real zero of f is an x-value a with f(a)=0—that corresponds to an x‑intercept (a, 0) on the graph. The point (0, −2) is a y‑intercept, not an x‑intercept, so it is not a zero. Likewise, not passing through the origin (0,0) does not imply there are no real zeros. The graph’s intercept at (−4, 0) gives the single real zero x = −4.
Reason: A real zero of f is an x-value a with f(a)=0—that corresponds to an x‑intercept (a, 0) on the graph. The point (0, −2) is a y‑intercept, not an x‑intercept, so it is not a zero. Likewise, not passing through the origin (0,0) does not imply there are no real zeros. The graph’s intercept at (−4, 0) gives the single real zero x = −4.
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