Questions: The graphs of the quadratic function (y=2 x^2) and the exponential function (y=2^x) are shown below. Considering only the domain shown on the graph, over which interval is the value of the exponential function greater than the value of the quadratic function? - (-2.5 leq x leq-0.75)

The graphs of the quadratic function (y=2 x^2) and the exponential function (y=2^x) are shown below. Considering only the domain shown on the graph, over which interval is the value of the exponential function greater than the value of the quadratic function? - (-2.5 leq x leq-0.75)
Transcript text: The graphs of the quadratic function $y=2 x^{2}$ and the exponential function $y=2^{x}$ are shown below. Considering only the domain shown on the graph, over which interval is the value of the exponential function greater than the value of the quadratic function? - $-2.5 \leq x \leq-0.75$
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Solution

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Solution Steps

Step 1: Analyze the graph

We are looking for the interval where the exponential function \(y = 2^x\) (represented by the slightly curved line) is greater than the quadratic function \(y = 2x^2\) (represented by the parabola). Visually, this means we are looking for the x-values where the graph of the exponential function is higher than the graph of the quadratic function.

Step 2: Identify the intersection points

The graphs intersect at approximately \(x = -0.75\) and \(x=2\), and also near \(x=4\) outside of the considered graph interval.

Step 3: Determine the interval

Between approximately \(x = -2.5\) and \(x = -0.75\), the exponential function is above the quadratic function. Also, between \(x=2\) and the right edge of the graph where x is slightly less than 4, the graph of the exponential function lies above that of the quadratic. We are looking for the interval stated in the options.

Final Answer

\\(\boxed{-2.5 \leq x \leq -0.75}\\)

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