Question

using the section of the graph shown, which of these potential roots of the function should you test first?

\\f(x) = 2x^3 - 9x^2 - 6x + 40\\

• -5
• -2
• 1
• 8

Explanation:

⚡ Using what you learned: Zeros and Multiplicity

Step 1: Identify roots from the graph

The roots (or zeros) of a function are the \(x\)-values where the graph crosses or touches the \(x\)-axis (where \(y = 0\)).

Looking at the provided graph:

• The graph crosses the \(x\)-axis on the negative side at \(x = -2\).
• The graph crosses the \(x\)-axis on the positive side at \(x = 2.5\) (between \(2\) and \(3\)) and at \(x = 4\).

Step 2: Compare with the given options

We are given the following potential roots to test:

• \(-5\)
• \(-2\)
• \(1\)
• \(8\)

Comparing these options with the visual \(x\)-intercepts on the graph, the only value that matches an actual intercept shown on the graph is \(-2\).

Answer:

-2