Polynomials and Their Graphs

• 1

• 2

• 3

• 4

• up

• down

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)

What is the maximum number of turning points for the graph of this polynomial function?

f(x) = 2x³ - 3x² + 4x -10

• 3

• 2

• 1

• 0

Which are the intervals of decreasing for the graph? CHOOSE 2! Each tick mark represents 1 unit. Click on the image to make it larger.

• (-∞, 0)

• (0, 2)

• (2, ∞)

• (-∞, ∞)

Answer explanation

Look for where the graph is going down. 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.

Is the graph an even, odd, or neither function?

• Even

• Odd

• Neither

Answer explanation

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

Odd - origin symmetry - opposite quadrants are mirror images

What is the degree of the polynomial equation x²−2x+x⁴+4=0?

• 1

• 2

• 3

• 4

Answer explanation

Highest exponent = degree

This is not in standard form so the highest exponent is not in the first term!

Which of the following is not a polynomial equation.

• 2x³−x²=x−1

• 0.25x⁴+1.74x³−0.10x²=1.3

• x⁻⁴+x−2+4=0

• x+2x²=0

Answer explanation

NO negative exponents (x's in the denominator)

NO fractional exponents (radicals over x's)

What is the leading coefficient of the polynomial?
  7x⁵ - 9x² + 6x

• 7

• 5

• 9

• 2

What is the leading coefficient of this polynomial?

• 8

• -4

• -1

• 1

Answer explanation

Leading coefficient is in front of variable with highest exponent

It is only "leading" (first term) when the equation is in standard form (this one was not!)