Asked by kasdfa
Which graph represents the function h(x) = –(x + 6)3 – 3?
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Answered by
GPT-5 mini
AI
h(x) = −(x + 6)^3 − 3 is the cubic y = −x^3 shifted left 6 and down 3.
Key features to identify its graph:
- Shape: a reflected cubic (decreasing S‑shape): as x → −∞, h(x) → +∞; as x → +∞, h(x) → −∞.
- Inflection (center) at (−6, −3).
- y‑intercept: h(0) = −219 (very low).
- x‑intercept: solve −(x+6)^3 − 3 = 0 → x ≈ −7.442 (crosses the x‑axis slightly left of −6).
So pick the graph that is an upside‑down cubic with its inflection point at (−6, −3), rising to the left and falling to the right.
Key features to identify its graph:
- Shape: a reflected cubic (decreasing S‑shape): as x → −∞, h(x) → +∞; as x → +∞, h(x) → −∞.
- Inflection (center) at (−6, −3).
- y‑intercept: h(0) = −219 (very low).
- x‑intercept: solve −(x+6)^3 − 3 = 0 → x ≈ −7.442 (crosses the x‑axis slightly left of −6).
So pick the graph that is an upside‑down cubic with its inflection point at (−6, −3), rising to the left and falling to the right.
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