For \(f(x)~=~(x~-~4)^3(x~+~2)^2\), describe the local behavior at every zero, including multiplicity, crossing or touching, and flattening.

Answer choices

Choose your path.

Preview only

x=4: m=3, crosses with flattening. x=−2: m=1, crosses without flattening.

x=4: m=2, touches and turns without flattening. x=−2: m=2, touches and turns without flattening.

x=4: m=3, crosses with flattening. x=−2: m=2, touches and turns with flattening.

x=4: m=3, crosses with flattening. x=−2: m=2, touches and turns without flattening.

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

Inside Gozunta

More than a preview

Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.

Discover Gozunta Try it now

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: Predict local zero behavior from multiplicity