Polynomials and Their Graphs

Does the graph represent a polynomial?

Smooth AND continuous?

• Yes, smooth and continuous

• No, smooth but not continuous

• No, continuous but not smooth

• No, neither continuous or smooth

Answer explanation

Polynomials must be smooth (no sharp corners) and continuous (must be able to draw graph without picking up pencil)

This graph is just 5 points. They are not connected, so while it looks smooth, there is no curve that is drawn!

What is another way to say "where a function crosses the x-axis"?

• x-intercept

• zero

• root

• all of these.

Tags

CCSS.HSF-IF.C.7C

Over what interval is this function constant?

• (-3,5)

• (-3, 4)

• (4,8)

• -5

Answer explanation

Look for where the graph is flat. Base the interval off the x-values.

Tags

CCSS.HSF-IF.C.7B

The shaded area represents

• Decreasing Interval

• Increasing Interval

• Constant Interval

Which is the interval of increasing for the graph? Assume there are arrows on the graph.

• (-∞, 1)

• (1, ∞)

• (-∞, ∞)

• (1, 5)

Answer explanation

Look for where the graph is going UP. Base the interval on the x-values. If there is an arrow pointing left, it goes back to negative infinity. If there is an arrow pointing right, it goes to positive infinity.

Which are intervals of increasing for the graph?

CHOOSE 2! Each tick mark represents 1 unit. Click on the image to make it larger.

• (-∞, -3)

• (-3, 0)

• (0, 2)

• (2, ∞)

Answer explanation

Look for where the graph is going UP. Base the interval on the x-values. If there is an arrow pointing left, it goes back to negative infinity. If there is an arrow pointing right, it goes to positive infinity.

Which is the interval of increasing for the graph? Assume the graph has arrows.

• (-2, ∞)

• (-∞, -2)

• (-4, ∞)

• (-∞, -4)

Answer explanation

Look for where the graph is going UP. Base the interval on the x-values. If there is an arrow pointing left, it goes back to negative infinity. If there is an arrow pointing right, it goes to positive infinity.

The function shown in the graph is:

• even

• odd

• neither even nor odd

• both even and odd

Answer explanation

Even - y-axis symmetry - fold in half vertically and it's a mirror image

Odd - origin symmetry - opposite quadrants are mirror images

Tags

CCSS.HSF.BF.B.3

The function in the graph is:

• even

• odd

• neither even nor odd

• both even and odd

Answer explanation

Even - y-axis symmetry - fold in half vertically and it's a mirror image

Odd - origin symmetry - opposite quadrants are mirror images

Tags

CCSS.HSF.BF.B.3

The function shown in the graph is:

• even

• odd

• neither odd nor even

• both odd and even

Answer explanation

Even - y-axis symmetry - fold in half vertically and it's a mirror image

Odd - origin symmetry - opposite quadrants are mirror images

Tags

CCSS.HSF.BF.B.3