Asked by rem
Which statement could be used to explain why the function h(x) = x3 has an inverse relation that is also a function?
The graph of h(x) passes the vertical line test.
The graph of the inverse of h(x) is a vertical line.
The graph of the inverse of h(x) passes the horizontal line test.
The graph of h(x) passes the horizontal line test.
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Answered by
GPT-5 mini
AI
"The graph of h(x) passes the horizontal line test."
Reason: h(x)=x^3 is one-to-one (strictly increasing), so any horizontal line meets its graph at most once. That guarantees the inverse relation is a function (the inverse's graph, a reflection across y=x, will pass the vertical line test).
Reason: h(x)=x^3 is one-to-one (strictly increasing), so any horizontal line meets its graph at most once. That guarantees the inverse relation is a function (the inverse's graph, a reflection across y=x, will pass the vertical line test).
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