Question

which key features were used to sketch this graph?
the function is continuous. the y - intercept is 0. the real zeros are between - 2 and - 1, and at 0. the relative maximum is at (1,4.5). the relative minimum is at (2.25, 1.75). as x→ - ∞, f(x)→+∞ and as x→+∞, f(x)→+∞.
the function is continuous. the y - intercept is 0. the real zero is between - 2 and - 1. the relative maximum is at (2.25, 1.75). the relative minimum is at (1,4.5). as x→ - ∞, f(x)→ - ∞ and as x→+∞, f(x)→+∞.
the function is continuous. the y - intercept is 0. the real zeros are between - 2 and - 1, and at 0. the relative maximum is at (2.25, 1.75). the relative minimum is at (1,4.5). as x→ - ∞, f(x)→+∞ and as x→+∞, f(x)→+∞.
the function is continuous. the y - intercept is 0. the real zero is between - 2 and - 1. the relative maximum is at (1,4.5). the relative minimum is at (2.25, 1.75). as x→ - ∞, f(x)→ - ∞ and as x→+∞, f(x)→+∞.

Explanation:

Step1: Analyze the continuity

Since the graph is a smooth curve without breaks, the function is continuous.

Step2: Check the y - intercept

The graph passes through the origin \((0,0)\), so the \(y\) - intercept is \(0\).

Step3: Locate the real zeros

The graph crosses the \(x\) - axis between \(-2\) and \(-1\) and at \(x = 0\).

Step4: Identify the relative extrema

The "highest" point (relative maximum) occurs at \((1,4.5)\) and the "lowest" point (relative minimum) occurs at \((2.25,1.75)\).

Step5: Determine the end - behavior

As \(x\to-\infty\) and \(x\to+\infty\), the graph goes up, so \(f(x)\to+\infty\) as \(x\to-\infty\) and \(x\to+\infty\).

Answer:

The function is continuous. The \(y\) - intercept is \(0\). The real zeros are between \(-2\) and \(-1\), and at \(0\). The relative maximum is at \((1,4.5)\). The relative minimum is at \((2.25,1.75)\). As \(x\to-\infty,f(x)\to+\infty\) and as \(x\to+\infty,f(x)\to+\infty\).