Question

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?
$-2.5 \leq x \leq -0.75$
$1 < x \leq 2.5$
$-0.5 \leq x < 1$
$1 < x \leq 1.5$

Explanation:

To solve this, we analyze the intervals where the exponential function's graph lies above the quadratic function's graph (from the given domain on the graph, though not shown here, we use the concept of function values: when \( y_{\text{exponential}} > y_{\text{quadratic}} \), the exponential is greater).

Analyzing each interval:

• For \( -2.5 \leq x \leq -0.75 \): Likely the quadratic is above the exponential (not the case).
• For \( -0.5 \leq x < 1 \): Quadratic may be above or equal (not the case).
• For \( 1 < x \leq 2.5 \): The exponential function’s value exceeds the quadratic’s (matches the condition).
• For \( 1 < x \leq 1.5 \): A subset of \( 1 < x \leq 2.5 \), but the broader correct interval is \( 1 < x \leq 2.5 \) (assuming the graph shows the exponential overtakes the quadratic here and stays above up to \( x = 2.5 \)).

Answer:

\( 1 < x \leq 2.5 \)