Try It

Practice Problems

Practice Problem #1

Tell the end behavior of the following function:

f(x) = −3x3 + 2x + 1

What is the leading coefficient?

Answer: −3x3

Is the degree even or odd?

Answer: odd

Is the leading coefficient positive or negative?

Answer: negative

A negative odd function starts _______blank and ends ________blank.

Answer: A negative odd function starts up and ends down.

As x → ___blank, f(x) → ___blank.

As x → ___blank, f(x) → ___blank.

Answer:

As x →− ∞, f(x) → ∞.

As x → ∞, f(x) → −∞.

Practice Problem #2

Look at the graph and describe the end behavior.

A graph of a quadratic function opening up with the vertex above the x-axis. The graph does not pass through the x-axis.

Answer:

x → −∞, f(x) → ∞, x → ∞, f(x) → ∞.

Practice Problem #3

Look at the graph and describe the end behavior.

A graph of a polynomial that starts down and ends up with 2 turning points and 1 x-intercept.

Answer:

x → −∞, f(x) → −∞, x → ∞, f(x) → ∞.

Practice Problem #4

Look at the graph and describe the end behavior.

A graph of a polynomial that starts up and ends up with 3 turning points and 3 x-intercepts.

Answer:

x → −∞, f(x) → ∞, x → ∞, f(x) → ∞.

Practice Problem #5

Look at the graph and describe the end behavior.

A graph of a polynomial that starts up and ends down with 2 turning points and 3 x-intercepts.

Answer:

x → −∞, f(x) → ∞, x → ∞, f(x) → −∞.

Practice Problem #6

Look at the graph and determine the number of turning points. Which answer is correct?

A graph of a quadratic function opening up with the vertex above the x-axis. The graph does not pass through the x-axis.

Answer: 1

Practice Problem #7

Look at the graph and determine the number of x-intercepts. Which answer is correct?

A graph of a quadratic function opening up with the vertex above the x-axis. The graph does not pass through the x-axis.

Answer: 0

Practice Problem #8

Look at the graph and determine the number of x-intercepts. Which answer is correct?

A graph of a polynomial that starts up and ends up with 3 turning points and 3 x-intercepts.

Answer: 3

Practice Problem #9

Look at the given function and determine the end behavior.

f(x) = 4x2 + x − 2

Answer:

x → −∞, f(x) → ∞, x → ∞, f(x) → ∞.

Practice Problem #10

Look at the given function and determine the maximum of x-intercepts.

f(x) = 4x2 + x − 2

Answer: 2

Practice Problem #11

Look at the given function and determine the maximum of turning points.

f(x) = 4x2 + x − 2

Answer: 1

Practice Problem #12

Look at the given function and determine the maximum of turning points.

f(x) = 4x2 + 6x 4 + x5 + 7

Answer: 5