1 a) If a graph has an HA (Horizontal asymtope) at y=0, does this mean it will always have no x-int? Explain. Provide equations to help support your answer b) If a graph has no x-int, will it always have a HA of y=0? Explain. Provide equations to help support your answer
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a) If a graph has an HA (Horizontal asymtope) at y=0, does this mean it will always have no x-int? Explain. Provide equations to help support your answer
b) If a graph has no x-int, will it always have a HA of y=0? Explain. Provide equations to help support your answer
a) Horizontal asymptotes are the lines parallel to the x-axis to which the graph of the function approaches as x tends to .
Therefore, a graph has a Horizontal asymptote at y=0 means that, the graph will not touch the line y=0 (x-axis).
Thus, a graph with a Horizontal asymptote at y=0, will not have x-intercepts.
For example, consider the equation .
The graph of the equation has horizontal asymptote at y=0. The curve never touches the x-axis and hence does not have any x-intercepts.
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