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Exercises Polynomials and factoring

Example 1 from Algebra and Trigonometry, 5.3 Graphs of Polynomial Functions

Recognizing Polynomial Functions

Which of the graphs in Figure 2 represents a polynomial function?

Two graphs in which one has a polynomial function and the other has a function closely resembling a polynomial but is not.

Figure 2

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
The graphs of $f$ and $h$ are graphs of polynomial functions. They are smooth and continuous.
The graphs of $g$ and $k$ are graphs of functions that are not polynomials. The graph of function $g$ has a sharp corner. The graph of function $k$ is not continuous.

How did it go?

PreviousDrawing Conclusions about a Polynomial Function from the Factors Next Finding the x-Intercepts of a Polynomial Function by Factoring

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 5.3, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.