Week 2: Homework - Key Features of Polynomial Functions

Look at the graph to describe the end behavior.

 $As\ x\ \rightarrow\ -\infty,\$   $f\left(x\right)\rightarrow\$  

•  $-\infty$  

•  $\infty$  

Answer explanation

 $As\ x\rightarrow-\infty$  means to look on the left side of the graph.  On the left side, the graph is going up.  To say the graph is going up, we write  $f\left(x\right)\rightarrow\infty$ . 

Look at the graph to describe the end behavior.

 $As\ x\ \rightarrow\ \infty,\$   $f\left(x\right)\rightarrow\$  

•  $-\infty$  

•  $\infty$  

Answer explanation

 $As\ x\rightarrow\infty$  means to look on the right side of the graph.  On the right side, the graph is going down.  To say the graph is going down, we write  $f\left(x\right)\rightarrow-\infty$  .

When you look at the graph, the ends of the graph are going in different directions.  This means that the degree of the polynomial is ...

• Odd

• Even

Answer explanation

Polynomials with odd degrees have end behaviors that go in different directions (one side up and one side down).  

Polynomials with even degrees have end behaviors that go in the same direction (both up or both down).

When you look at the graph, you can tell that the right side of the graph is pointing down.  What does that tell you about the leading coefficient?

• Positive

• Negative

Answer explanation

Polynomials with positive leading coefficients have right sides that point up.

Polynomials with negative leading coefficients have right sides that point down.

Where is the x-intercept of the graph?

• -1.07

• 0.97

• -2.99

• -5

Answer explanation

x-intercepts occur when the graph crosses the x-axis

Where is the y-intercept of the graph?

• -1.07

• 0.97

• -2.99

• -5

Answer explanation

y-intercepts occur when the graph crosses the y-axis

Where does the relative minimum occur?

• (-1.07, 0)

• (0, -5)

• (0.97, -2.99)

Answer explanation

When you are looking for relative minimums, look for a "valley" or "low point" on the graph.  

Where does the relative maximum occur?

• (-1.07, 0)

• (0, -5)

• (0.97, -2.99)

Answer explanation

When you are looking for relative maximums, look for a "hill" or "high point" on the graph.  

Choose all that apply.  

Which intervals on the graph are decreasing?

•  $\left(-\infty,\ 0\right)$  
  

•  $\left(0,\ 0.97\right)$  
  

•  $\left(0.97,\ \infty\right)$  
  

Answer explanation

The intervals are listed only with the x-coordinates.  Sections of the graph are decreasing if it is going down as you scan the graph from left to right.

Choose all that apply.  

Which intervals on the graph are increasing?

•  $\left(-\infty,\ 0\right)$  
  

•  $\left(0,\ 0.97\right)$  
  

•  $\left(0.97,\ \infty\right)$  
  

Answer explanation

The intervals are listed only with the x-coordinates.  Sections of the graph are increasing if it is going up as you scan the graph from left to right.