A coordinate plane shows the x-axis and the y-axis ranging from negative 5 to 5, in increments of 0.5 units, but labeled at every unit. An upward-opening parabola is plotted on the graph.
The parabola represents the graph of the quadratic function f(x)=2x2+6x+4.5
. Which of the following describes the domain of this function?
(1 point)
Responses
x≤0
x is less than or equal to 0
−1.5≤x≤0
negative 1.5 less-than-or-equal-to x less-than-or-equal-to 0
x≥0
x is greater than or equal to 0
−∞<x<∞
negative infinity is less than x comma x is less than infinity
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1 answer
The function \( f(x) = 2x^2 + 6x + 4.5 \) is a quadratic function, which is defined for all real numbers. The domain of a quadratic function is typically all real numbers unless there are restrictions (like division by zero or square roots of negative numbers, which do not apply here).
Therefore, the correct response describing the domain of this function is:
\(-\infty < x < \infty\) (negative infinity is less than x, comma x is less than infinity).
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