Problem preview

F-IF.7.c Warmup M3-025-A07-V02

Graph polynomial functions using zeros, factorizations, and end behavior.

Match a factored polynomial to its x-intercepts, multiplicities, and end behavior

Problem

For \(f(x)~=~-(x~-~3)(x~+~1)(x~-~4)\), state the \(x\text{-}\text{intercepts}\), whether the graph crosses or touches at \(\text{each}~\text{one}\), and the left and right end behavior.

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The graph crosses the x-axis at x = -1, x = 3, and x = 4, and it falls to the left and rises to the right.

The graph crosses the x-axis at x = -1, x = 3, and x = 4, and it rises to the left and falls to the right.

The graph crosses the x-axis at x = -3, x = 1, and x = 4, and it rises to the left and falls to the right.

The graph touches the x-axis at x = -1, x = 3, and x = 4, and it rises to the left and falls to the right.

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Curriculum context

Course: Math III
Standard: F-IF.7.c
Category: Functions
Domain: Interpreting Functions
Objective: Graph polynomial functions using zeros, factorizations, and end behavior.
Problem type: Match a factored polynomial to its x-intercepts, multiplicities, and end behavior