Free Printable Polynomial Functions: End Behavior/Degree/Leading Coefficients

1.

Determine end behavior of function with the given graph

a)

$x\rightarrow-\infty;\ f\left(x\right)\ \rightarrow\ -\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow+\infty$

b)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow+\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow-\infty$

c)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow-\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow\ -\infty$

d)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow+\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow+\infty$

2.

Determine end behavior of function with the given graph

a)

$x\rightarrow-\infty;\ f\left(x\right)\ \rightarrow\ -\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow+\infty$

b)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow+\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow-\infty$

c)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow-\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow\ -\infty$

d)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow+\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow+\infty$

3.

Determine end behavior of function with the given graph

a)

$x\rightarrow-\infty;\ f\left(x\right)\ \rightarrow\ -\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow+\infty$

b)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow+\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow-\infty$

c)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow-\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow\ -\infty$

d)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow+\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow+\infty$

4.

What is the leading coefficient?

a)

Positive

b)

Negative

c)

Odd

d)

Even

5.

What of the following is a correct end behavior?

a)

as\ x\ \longrightarrow\infty,\ f\left(x\right)\longrightarrow\ \infty\

b)

$as\ x\ \longrightarrow\infty,\ f\left(x\right)\longrightarrow-\infty$

6.

What of the following is a correct end behavior?

a)

as\ x\ \longrightarrow-\infty,\ f\left(x\right)\longrightarrow\ \infty\

b)

$as\ x\ \longrightarrow-\infty,\ f\left(x\right)\longrightarrow-\infty$

7.

In the above graph complete the following end behavior:
$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow$ _____

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

a)

-∞
-∞

b)

+∞
-∞

c)

-∞
+∞

d)

+∞
+∞

8.

In the above graph complete the following end behavior:
$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow$ ____

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

a)

-∞
-∞

b)

+∞
-∞

c)

-∞
+∞

d)

+∞
+∞

9.

Describe the end behavior of the function.

$f\left(x\right)=4x^{10}$

a)

L: down and R: down

b)

L: down and R: up

c)

L: up and R: down

d)

L: up and R: up

10.

Determine the end behavior of the graph.

a)

As x→ -∞, y→ -∞
As x→ +∞, y→ +∞

b)

As x→ -∞, y→ -∞
As x→ +∞, y→ -∞

c)

As x→ -∞, y→ +∞
As x→ +∞, y→ +∞

d)

As x→ -∞, y→ +∞
As x→ +∞, y→ -∞

11.

What is the end behavior for the graph?

a)

x → ⁻∞, y→ ⁻∞ and

x→ ∞, y→ ⁻∞

b)

x → ⁻∞, y→ ∞ and

x→ ∞, y→ ∞

c)

x → ⁻∞, y→ ⁻∞ and

x→ ∞, y→ ∞

d)

x → ⁻∞, y→ ∞ and

x→ ∞, y→ ⁻∞

12.

Describe the end behavior for the graph.

a)

x → ⁻∞, y→ ⁻∞ and

x→ ∞, y→ ⁻∞

b)

x → ⁻∞, y→ ∞ and

x→ ∞, y→ ∞

c)

x → ⁻∞, y→ ⁻∞ and

x→ ∞, y→ ∞

d)

x → ⁻∞, y→ ∞ and

x→ ∞, y→ ⁻∞

13.

What is the degree of the polynomial function whose graph appears below?

a)

1

b)

2

c)

3

d)

4

14.

What is the degree of the polynomial function

P(x)=3x⁴-7x²-2x⁷-x+4? (Hint: Write the Polynomial in order from biggest exponent to smallest exponent)

a)

4

b)

7

c)

2

d)

1

15.

What is the degree of the function graphed here?

a)

2

b)

3

c)

4

d)

5

16.

How many turning points does the graph of

P\left(x\right)=x^4-2x^2+x+1

have?

a)

4

b)

less than 4

c)

more than 4

17.

This graph is a(n)...

a)

Third degree polynomial

b)

Sixth degree polynomial

c)

Even function

d)

Fifth degree polynomial

18.

If the degree of the function is even, then...

a)

The end arrows point in the same direction

b)

The end arrows point in opposite directions

c)

There is no way to tell what the ends of the graph do.

19.

If the degree of the function is odd, then...

a)

The end arrows point in the same direction

b)

The end arrows point in opposite directions

c)

There is no way to tell what the ends of the graph do.

20.

Even or Odd degree?

a)

even

b)

odd

21.

Which graph has an even degree?

a)

b)

c)

22.

Check all the even degree polynomials:

a)

b)

c)

d)

e)

23.

What is the sign of the leading coefficient of the polynomial function whose graph appears below?

a)

positive

b)

negative

24.

Is the leading coefficient positive or negative

a)

positive

b)

negative

25.

What is the leading coefficient?

Remember to look at your roots, multiplicity, and end behavior!!

Use your notes!

a)

Positive

b)

Negative

26.

Which graph has a negative leading coefficient?

a)

b)

c)

27.

Based on the end behavior which option best describes the leading term?

Remember to look at your roots, multiplicity, and end behavior!!

Use your notes!

a)

negative coefficient, even degree

b)

negative coefficient, odd degree

c)

negative degree, odd coefficient

d)

negative degree, even coefficient

28.

Which best describes the graph

a)

a polynomial with even degree and negative leading coefficient

b)

a polynomial with even degree and positive leading coefficient

c)

a polynomial with odd degree and negative leading coefficient

d)

a polynomial with odd degree and positive leading coefficient

29.

Match the following End Behavior to their Graphs

a)

1.

Degree is Odd, Leading Coefficient is Negative

b)

2.

Degree is Odd, Leading Coefficient is Positive

c)

3.

Degree is Even, Leading Coefficient is Negative

d)

4.

Degree is Even, Leading Coefficient is Positive

30.

What is the end behavior of the graph of

P\left(x\right)=2x^3+3x^2-2x+1

?

a)

The graph falls to the left and rises to the right

b)

The graph rises to the left and falls to the right

c)

The graph rises to both ends

d)

The graph falls to both ends

31.

What is the end behavior of

$h(x)=-8x^5+22x^4-4x^3+11x-9$

a)

up/down

b)

down/up

c)

up/up

d)

down/down

32.

What is the end behavior of

$g\left(x\right)=-2x^6+2x^5-12x-6$

a)

up/down

b)

down/up

c)

down/down

d)

up/up

33.

What is the end behavior of

$k(x)=7x^9+5x^6-4x-22$

a)

UP/UP

b)

Down/Down

c)

Up/Down

d)

Down/UP

34.

What is the end-behavior of the function $y=-7x^4+7x^3-9x^2+10$ ?

a)

as $x\rightarrow-\infty f\left(x\right)\rightarrow-\infty$
as $x\rightarrow\infty\ f\left(x\right)\rightarrow-\infty$

b)

as $x\rightarrow-\infty\ f\left(x\right)\rightarrow-\infty$
as $x\rightarrow\infty\ f\left(x\right)\rightarrow\infty$

c)

as $x\rightarrow-\infty\ f\left(x\right)\rightarrow\infty$
as $x\rightarrow\infty\ f\left(x\right)\rightarrow-\infty$

d)

as $x\rightarrow-\infty\ \ f\left(x\right)\rightarrow\infty$
as $x\rightarrow\infty\ f\left(x\right)\rightarrow\infty$

35.

What is the end behavior of the graph of

P\left(x\right)=-2x^4+3x^2-2x+1

?

a)

The graph falls to the left and rises to the right

b)

The graph rises to the left and falls to the right

c)

The graph rises to both ends

d)

The graph falls to both ends

36.

Which of these is in Standard Form?

a)

$4x^2+12x-13x^3$

b)

$5-3x$

c)

$2x^4-12x^2+9\ -5x$

d)

$5x^5+4x^{\text{4}}+12x^3-23x+15$

37.

What is the leading coefficient in the polynomial $3x^2-5x^7-45$ ?

(Hint: think about standard form)

a)

3

b)

-5

c)

-45

d)

7

38.

Which of the following is a 5th degree trinomial with a leading coefficient of -2?

a)

-2x⁵ + 3x - 1

b)

5x^-2 +3x - 1

c)

2x⁵ + 3x⁴ + 2x³ + x² - 10

d)

2x + 5

Polynomial Functions: End Behavior/Degree/Leading Coefficients

Total questions: 38

Worksheet time: 38mins

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