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
enot [183]
3 years ago
15

What best describes the asymptote of an exponential function of the form f(x)=b^x?

Mathematics
2 answers:
horrorfan [7]3 years ago
6 0

It depends on the value of b


Exponential functions are defined for positive values of the base [ŧex] b [/tex]. Also, they're not defined if b=1, or at least let's say that this is a trivial case, since it is the constant function 1.


Case 0<b<1:

If the base sits between 0 and 1, the exponential function is constantly decreasing. The explanation is quite intuitive, assume for the sake of simpleness that b is rational. If it sits between 0 and 1, it means that it can be written as a fraction p/q, with p<q. So, if you give a large exponent to b, you obtain


\frac{p^x}{q^x},\quad p^x \ll q^x \text{ as } x \to \infty


On the other hand, if you consider negative exponents, you switch numerator and denominator and then raise to the same exponent the fraction q/p, which gets larger and larger.


So, if 0<b<1, we have


\lim_{x \to -\infty} b^x = \infty,\qquad \lim_{x \to \infty} b^x = 0


and thus 0 is a horizontal asymptote as x tends to (positive) infinity.


Case b>1:

This case is very similar, except all roles are inverted. Now you start with a fraction p/q where p>q. So, with positive, large exponents you get


\frac{p^x}{q^x},\quad p^x \gg q^x \text{ as } x \to \infty


And as before, negative exponents switch numerator and denominator, so the fraction becomes q/p and thus you have


\lim_{x \to -\infty} b^x = 0,\qquad \lim_{x \to \infty} b^x = \infty


So, again, 0 is a horizontal asymptote, but this time for x tending towards negative infinite.

Thepotemich [5.8K]3 years ago
4 0

Horizontal asymptote at y=0

You might be interested in
If six women paint a fence in two days, how long does it take for two women to paint the fence?
ivanzaharov [21]

Answer:

6 days

Step-by-step explanation:

I know this because you would divide 6 women by 3 to get two women so you would multiply the two days by 3 to get 6 days

4 0
3 years ago
Two students have partially simplified the same expression. Audrey's work: ( x3y−2 22x−5y3 ) 3 = ( x8y−5 22 ) 3 = x24y−15 26 Dav
Crank

Answer:

<h3>-<u>Aubrey first applied division of like bases by subtracting the exponents.</u></h3><h3>-<u>Next David will apply the quotient of powers.</u></h3><h3><u>-Aubrey's work is correct .</u></h3><h3><u>-The correct simplified answer is x^24/64y^15</u></h3>
4 0
3 years ago
Read 2 more answers
Dividing exponents in this equation
jeka94

Answer:

18x^5y

Step-by-step explanation:

Divide 36 by 2 first : 18

since you are dividing, you subtract the exponents:

x^8 - x^3= x^5

y^4-y^3= y^1 but you usually just write y

8 0
3 years ago
Please help!! will give brainliest!
raketka [301]

Answer:

Angle EDC = Angle ADC

(Reflexive property)

ABD ~ ECD because all angles are congruent

If two are congruent, third one has to be as well since total angle is 180 each

3 0
3 years ago
A study is undertaken to find out how much water, in gallons, is in Lake Michigan. Which type of data will the study analyze?
Drupady [299]
<span>A.
continuous data
gallons in a lake would be continuous data because it is not counted in integers but measured by how much volume is in the lake. 
</span>
8 0
3 years ago
Other questions:
  • How do i find the scale factor on a graph?
    9·1 answer
  • Rachel sells internet subscriptions by telephone. She receives 12% of the first $800 and 16% on the balance over $800. Last mont
    5·2 answers
  • Someone please help.
    14·1 answer
  • 2/3 4/9 5/6 7/12 least to greatest
    9·1 answer
  • In triangle ABC, a = 9, c = 5, and angle B = 120°. Find the measure of angle A to the nearest degree. Show your work.
    13·2 answers
  • PLEASE HELP FAST!!! ITS EASY BUT NOT FOR ME!!
    5·2 answers
  • Tính giá trị 2a+ 3=? với a=1
    11·1 answer
  • Find the values of x that make m parallel to n.<br> Please help!!
    10·1 answer
  • Santa needs 600 toys. 175 toys have already
    9·1 answer
  • On a coordinate plane, a straight red line with a negative slope, labeled g of x, A graph shows the number of texts, numbered 10
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!