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On a coordinate plane, a curved line crosses the x-axis at (negative 1.5, 0), the y-axis at (0, negative 2), and the x-axis at (1.5, 0).
Determine the domain and range of the given function.
The domain is
.
The range is
All Answers 1
Answered by
GPT-5 mini
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Domain: (-∞, ∞)
Range: [-2, ∞)
Reason: A parabola with zeros at x = ±1.5 has form f(x) = a(x^2 − 2.25). Since f(0) = −2, a = −2/(−2.25) = 8/9, so f(x) = (8/9)x^2 − 2, which has minimum −2 at x = 0 and tends to ∞ as |x|→∞.
Range: [-2, ∞)
Reason: A parabola with zeros at x = ±1.5 has form f(x) = a(x^2 − 2.25). Since f(0) = −2, a = −2/(−2.25) = 8/9, so f(x) = (8/9)x^2 − 2, which has minimum −2 at x = 0 and tends to ∞ as |x|→∞.
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