1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
liberstina [14]
3 years ago
5

Determine the end behavior of the following monomial functions. (That is, does the function output increase without bound (→[inf

inity]) or decrease without bound (→−[infinity]) as the input increases/decreases without bound?)
Suppose f(x)=x2.

As x→[infinity], f(x)→
As x→−[infinity], f(x)→
Suppose g(x)=x3.

As x→[infinity], g(x)→
As x→−[infinity], g(x)→
Suppose h(x)=−6x3.

As x→[infinity], h(x)→
As x→−[infinity], h(x)→
Mathematics
1 answer:
rosijanka [135]3 years ago
5 0

Answer:

a) f(x) = x²

As x→[infinity], f(x)→[infinity]

As x→−[infinity], f(x)→[infinity]

For this function, f(x) increases without bound as the input increases or decreases without bound. The graph of this function would be symmetric about the y-axis.

b) g(x) = x³

As x→[infinity], g(x)→[infinity]

As x→−[infinity], g(x)→-[infinity]

g(x) increases without bound as the input x increases without bound and decreases also without bound as input x decreases without bound. The graph of this function would be symmetric about the origin.

c) h(x)=−6x³.

As x→[infinity], h(x)→-[infinity]

As x→−[infinity], h(x)→[infinity]

h(x) decreases without bound as the input x increases without bound and increases without bound as input x decreases without bound. The graph of this function would also be symmetric about the origin.

Step-by-step explanation:

Normally, end behaviours predict the nature of the graphs of functions (especially as the values of x become very large, both in the positive and negative sense.

f(x) = x²

As x →[infinity],

f(x) = (∞)² → ∞

f(x) →[infinity]

And as x →−[infinity],

f(x) = (-∞)² → ∞

f(x) →[infinity]

For this function, f(x) increases without bound as the input increases or decreases without bound. The graph of this function would be symmetric about the y-axis.

b) g(x) = x³

As x→[infinity],

g(x) = (∞)³ → ∞

g(x)→[infinity]

As x→−[infinity],

g(x) = (-∞)³ → -∞

g(x)→−[infinity]

g(x) increases without bound as the input x increases without bound and decreases also without bound as input x decreases without bound. The graph of this function would be symmetric about the origin.

c) h(x)=−6x³.

As x→[infinity],

h(x) = -6(∞)³ → -6(∞) → -∞

h(x)→-infinity]

As x→−[infinity],

h(x) = -6(-∞)³ → -6(-∞) → ∞

h(x)→[infinity]

h(x) decreases without bound as the input x increases without bound and increases without bound as input x decreases without bound. The graph of this function would also be symmetric about the origin.

Hope this Helps!!!

You might be interested in
Determine whether the two angles in each figure are complementary, supplementary, or neither.
snow_tiger [21]
1.linear pair
2. neither
3. vertical
4. neither
5. vertical
6. neither
7. linear pair
8. neither

Their starting from up to down not side to side
7 0
3 years ago
Read 2 more answers
Can you solve this for me please​
Hatshy [7]

Answer:

Graph 1

Step-by-step explanation:

f(x) = __

In this equation (f(2) = 4) the 2 is the x value. All this question is asking is which graph shows a y value of 4 when x is 2.

4 0
3 years ago
About how much paint does Neil have in all
liq [111]
1/3 = 10/30
1/5 = 6/30
1/2 = 15/30
10+6+15= 31/30
31/30 = 1 1/30
It would be Less Than 1 1/2 Gallons
8 0
3 years ago
ITS FOR A TEST HELPPPPP
Marrrta [24]

Answer:

top right

Step-by-step explanation:

5 0
3 years ago
Determine the area of the coin to the nearest tenth.
Snowcat [4.5K]

Answer:

I THINK 20 mm

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Other questions:
  • A certain fungus grows in a circular shape. Its diameter in inches after t weeks is given below 6 -(50/t^2+ 10). What is the squ
    13·1 answer
  • Which expressions go in which box?
    7·1 answer
  • Find the minimum and maximum possible areas for a rectangle measuring 4.15 cm by 7.34 cm. Round to the nearest hundredth. A. min
    13·2 answers
  • What is each of the expression written using each base only once? 10^10 x 10^10
    13·1 answer
  • . Una persona desea realizar una pintura para su próxima exposición en donde esta tenga tres colores fluorescentes y dos colores
    7·1 answer
  • In a group of 50 people 28% of them has flue shots done. What is the probability to choose from this group 15 people that didn't
    15·1 answer
  • ‼️‼️I REALLY NEED THIS ASAP PLS I’ll give 60 pts thank you
    13·1 answer
  • 3) What is the shape of the graph of the equation y = 5x – 2?​
    12·1 answer
  • Your long distance service provider charges you $.06 per minute plus a monthly access fee of $4.95. For referring a friend, you
    12·1 answer
  • Topic: Absolute Value Equations and Inequalities
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!