Question

1. which of the following is the graph of \\(y = (x + 1)(x - 1)(x - 5)\\)?

Explanation:

Identify the zeros of the function

Using the Zeros of a Function from Graph knowledge point

$$
LATEXBLOCK0
$$

Determine the end behavior of the polynomial

Using the End Behavior of Polynomials knowledge point

$$
LATEXBLOCK1
$$

Analyze the given graph options

We compare the calculated properties with the visible graphs:

• The first graph has \(x\)-intercepts at \(x = -1\), \(x = 1\), and \(x = 5\).
• The first graph starts in the third quadrant (bottom-left) and ends in the first quadrant (top-right), which matches the positive cubic end behavior.
• The second graph has a negative leading coefficient behavior (starts high, ends low).
• The third graph is a parabola, which represents a quadratic function rather than a cubic function.

Therefore, the first graph is the correct representation.

Answer:

• (A) The first graph, which crosses the x-axis at -1, 1, and 5, and goes upwards to the right. (Correct answer)
• (B) The second graph, which goes downwards to the right.
• (C) The third graph, which is a parabola.