Question

Question was provided via image upload.

Explanation:

Identify the zeros of the function

Using the Zeros of a Function from Graph and Polynomial Factored Form knowledge points

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LATEXBLOCK0
$$

Determine the y-intercept

Using the Polynomial Factored Form knowledge point

$$
LATEXBLOCK1
$$

Analyze the end behavior

Using the End Behavior of Polynomials knowledge point

$$
LATEXBLOCK2
$$

Evaluate the shown graph

The displayed graph is a parabola with a vertex at approximately \((0, 5)\) and zeros near \(-2.2\) and \(2.2\). Since the given function \(y = (x+1)(x-1)(x-5)\) is a cubic polynomial with three distinct real roots, its graph must be a cubic curve crossing the x-axis at \(x = -1\), \(x = 1\), and \(x = 5\). Therefore, the visible graph is incorrect.

Answer:

The correct graph of the cubic function \(y = (x + 1)(x - 1)(x - 5)\) must have:

• Three x-intercepts at \(x = -1\), \(x = 1\), and \(x = 5\).
• A y-intercept at \((0, 5)\).
• End behavior where the graph goes down to the left (\(y \to -\infty\) as \(x \to -\infty\)) and up to the right (\(y \to \infty\) as \(x \to \infty\)).

The graph shown in the image is a parabola (quadratic function) and is not the correct graph.