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 -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 meets the -axis at the points , 0, and 3. The vertical lines, together with the -axis, divide the plane into eight regions (a)–(h).

In which regions does the graph of 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 -axis an even number of times.

• Afalse
• Btrue

Q5:

Determine whether the following statement is true: If the graph of a polynomial meets the -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