Worksheet: Predicting Graphs of Polynomials

In this worksheet, we will practice observing the links between the degree of a polynomial function, the x-intercepts of its graph, and the roots of the function.

Q1:

Determine whether the following statement is true: If the graph of a polynomial does NOT cross the 𝑥 -axis, then the degree of the polynomial is even.

  • A true
  • B false

Q2:

The given graph represents a polynomial function.

What can be said about the degree of this polynomial?

  • A The degree is exactly 4.
  • B The degree is at most 4.
  • C It is not possible to say anything.
  • D The degree is at least 4.

Q3:

The graph of 𝑇 ( 𝑥 ) = 𝑥 ( 𝑥 + 1 ) ( 𝑥 3 ) 2 meets the 𝑥 -axis at the points 1 , 0, and 3. The vertical lines, together with the 𝑥 -axis, divide the plane into eight regions (a)–(h).

In which regions does the graph of 𝑇 lie?

  • A (a), (b), (g), (h)
  • B (e), (f), (c), (h)
  • C (e), (f), (c), (d)
  • D (a), (b), (g), (d)
  • E (a), (f), (c), (h)

Q4:

Determine whether the following statement is true: If the degree of a polynomial is even, then its graph meets the 𝑥 -axis an even number of times.

  • Afalse
  • Btrue

Q5:

Determine whether the following statement is true: If the graph of a polynomial meets the 𝑥 -axis an even number of times, then the degree of the polynomial is even.

  • A false
  • B true

Q6:

Determine whether the following statement is true: If the graph of a function meets the axis infinitely many times, then the function is not polynomial.

  • A true
  • B false

Q7:

True or False: If the graph of a polynomial function has a maximum but no minimum, then the degree of the polynomial is even.

  • A True
  • B False

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