Free Printable Features of Polynomial Functions

1.

What is the Relative Maximum of this function?

a)

x = 5

b)

Infinity

c)

There is no Relative Maximum.

d)

2.5 and it occurs at x = 5

2.

Identify the intervals where the function is positive and where it is negative.

a)

positive (-1, ∞) and negative (-∞, -1)

b)

positive nowhere and negative (-1, -4)

c)

positive (-∞,-3) and (1,∞) and negative (-3,1)

d)

positive (-∞,∞) and negative (-4,∞)

3.

Identify where the function is increasing and where it is decreasing.

a)

increasing (-1, ∞) and decreasing (-∞,-1)

b)

increasing (-∞, -1) and decreasing (-1, ∞)

c)

increasing (-∞,∞) and decreasing nowhere

d)

increasing (-1, -4) and decreasing (-3, 1)

4.

Where is the function positive and where is it negative?

a)

positive (-2,1) and (3,∞) and negative (-∞,-2) and (1,3)

b)

positive (-∞,-1) and (2,∞) and negative (-1,2)

c)

positive (-1,4) and negative (2,-2)

d)

positive (∞,3) and (1,-2) and negative (3,1) and (-2,-∞)

5.

When is this function decreasing?

a)

(-3, 3)

b)

(-∞, -3) U (3, ∞)

c)

(-∞, -3] U [3, ∞)

d)

[-3, 3]

6.

On which interval(s) is the given function increasing?

a)

(-∞, 2) U (-2, ∞)

b)

(-2, 2) U (-2, ∞)

c)

(-∞, -2) U (0.5, ∞)

d)

(0, 2) U (0.5, ∞)

7.

When is this function increasing?

a)

-3<x<3

b)

-2.5<x<2.5

c)

x>2.5

d)

x>3

8.

Where is the decreasing?

a)

( −∞, −2.55) U (0, 2.55)

b)

(∞, −6.25) U (36, −6.25)

c)

( −∞, −2.55] U [0, 2.55]

d)

(−∞, 0)

9.

The blue dot on this graph represents a(n)...

a)

Absolute Maximum

b)

Absolute Minimum

c)

Relative Maximum

d)

Relative Minimum

10.

What are the Relative Maxima of this graph?

a)

$3.9$ only

b)

$5$ only

c)

$-3.3$ and $-2.5$

d)

$5$ and $3.9$

e)

No Relative Maxima

11.

Identify where the function is positive.

a)

$\infty<x<-5\ \ ,\ \ \ \infty<x<0$

b)

$-5<x<0\ \ ,\ \ \ x>6$

c)

$\infty<x<-5\ \ ,\ 0<x<6$

d)

$x>-5\ \ ,\ \ \ x<6$

12.

Identify where the function is positive.

a)

All Real Numbers

b)

$x<-3$

c)

$-3<x<3$

d)

$\infty<x<-3\ ,\ \ 3<x<\infty$

13.

What is the decreasing interval on the function shown?

a)

$-\infty<x\le1$

b)

$-\infty<x\le2$

c)

$2\le x<\infty$

d)

$1\le x<\infty$

14.

Over which intervals is the function increasing?

a)

−4 < x < −2 and −1 < x < 1

b)

−4 < x < −2 and 0 < x < 2

c)

−2 < x < 0 and 2 < x < 4

d)

−2 < x < −1 and 2 < x < 4

15.

Where is the function decreasing?

a)

(-∞, -1)

b)

(-1, ∞)

c)

(-∞, 3)

d)

(-∞, ∞)

16.

For what intervals of x is f(x) positive?

a)

x ≤ -1

b)

x ≥ -1

c)

-3 < x < 1

d)

0 ≤ x ≤ 1.5

17.

Identify where the function is positive.

a)

$-3<x<3$

b)

All Real Numbers

c)

$x<-3,\ \ x>3$

18.

Identify where the function is negative.

a)

$x<-7,\ \ \ x\ >5$

b)

$-7<x<-3,\ \ \ x\ >5$

c)

$x<-7,\ \ \ -3<x<5$

d)

$-7<x<5$

19.

What are the extrema of the graph?

a)

Max = (0,-4)

Min = (-1.5,0) and (1.5, 0)

b)

Max = (0,1.5) and (0, -1.5)

Min = (-4,0)

c)

Max = (-1.5,0) and (1.5, 0)

Min = (0,-4)

d)

Max = (-4,0)

Min =(0,1.5) and (0, -1.5)

20.

What are the increasing and decreasing intervals of the graph?

a)

Increasing = (-1.5, 0) & (1.5, ∞)

Decreasing = (-∞, -1.5) & (0, 1.5)

b)

Increasing = (-∞, -1.5) & (0, 1.5)

Decreasing = (-1.5, 0) & (1.5, ∞)

c)

Increasing = (-∞, -1.5) & (1.5, ∞)

Decreasing = (-1.5, 0) & (0, 1.5)

d)

Increasing = (-1.5, 0) & (0, 1.5)

Decreasing = (-∞, -1.5) & (1.5, ∞)

21.

What are the increasing and decreasing intervals of the graph?

a)

Increasing = (-∞,-3), (-1,2), (4, ∞)

Decreasing = (-3,-1), (2,4)

b)

Increasing = (-3,-1), (2,4)

Decreasing = (-∞,-3), (-1,2), (4, ∞)

c)

Increasing = (-∞,-3), (-1,2),

Decreasing (-3,-1), (2,4), (4, ∞)

d)

Increasing = (-∞, 2), (-3, 1), (-1, ∞)

Decreasing (2, -3), (1, -1)

22.

What are the extrema of the graph?

a)

Max = (2, -3), (1, 2)

Min = (-3, -1), (-1, 4)

b)

Max = (-3, -1), (-1, 4)

Min = (2, -3), (1, 2)

c)

Max = (-1, -3), (4, -1)

Min = (-3, 2), (2, 1)

d)

Max = (-3, 2), (2, 1)

Min = (-1, -3), (4, -1)

23.

How many increasing/decreasing intervals are there in this graph?

a)

2 max, 2 min

b)

3 max, 2 min

c)

2 man, 3 min

d)

3 increasing intervals, 2 decreasing intervals

e)

2 increasing intervals, 3 decreasing intervals

24.

as x increases, y does what

a)

increases

b)

decreases

c)

stays the same

d)

approaches 0

25.

as x increases, y _____________

a)

increases

b)

decreases

c)

stays the same

d)

approaches 4

Features of Polynomial Functions

Total questions: 25

Worksheet time: 2hrs 12mins

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