Problem preview

F-IF.7.c Warmup M3-025-A07-V03

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

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

Problem

For \(f(x)~=~(x^2~+~1)(x~-~5)\), state all real \(x\text{-}\text{intercepts}\) and the left and right end behavior.

Answer choices

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The graph has its only real x-intercept at x = 5, and it rises to the left and falls to the right.

The graph has x-intercepts at x = -1 and x = 5, and it falls to the left and rises to the right.

The graph has x-intercepts at x = -5 and x = 1, and it falls to the left and rises to the right.

The graph has its only real x-intercept at x = 5, and it falls to the left and rises 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