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
lyudmila [28]
3 years ago
9

What is the asymptote for the graph of this logarithmic function? f(x) = log3(x – 1)

Mathematics
2 answers:
Pepsi [2]3 years ago
7 0

Answer:

Vertical Asymptote:

x=1

Horizontal asymptote:

it does not exist

Step-by-step explanation:

we are given

f(x)=log_3(x-1)

Vertical asymptote:

we know that vertical asymptotes are values of x where f(x) becomes +inf or -inf

we know that any log becomes -inf when value inside log is zero

so, we can set value inside log to zero

and then we can solve for x

x-1=0

we get

x=1

Horizontal asymptote:

we know that

horizontal asymptote is a value of y when x is +inf or -inf

For finding horizontal asymptote , we find lim x-->inf or -inf

\lim_{x \to \infty}  f(x)= \lim_{x \to \infty}log_3(x-1)

\lim_{x \to \infty}  f(x)=log_3(\infty-1)

\lim_{x \to \infty}  f(x)=undefined

so, it does not exist

inessss [21]3 years ago
7 0

The asymptote for the graph of this logarithmic function is at x = 1

<h3>Further explanation </h3>

An asymptote of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity. Whereas the logarithm is the inverse function to exponentiation and any exponential function can be expressed in logarithmic form.

First we solve log_3(x-1) = 0

Raise both sides of the equation by the base of the logarithm:

3^(log_3(x-1)) = 3^0

Because any non-zero number raised to 0 equals 1, the right side simplifies to 1

By using the property of logarithms that b^{(logbx)} = x, where the left side simplifies to x-1

The equation is simply: x - 1 = 1

So x = 2.

The domain of a logarithmic function is the set of all positive real numbers. For example f(x) = log x also has an asymptote at x =0. But, since our function is log (x-1), we will move the asymptote to the right by 1 unit. Thus, x = 1.  Which explains that the graph will never touch at x=1 which will be the vertical asymptote.

<h3>Learn more</h3>
  1. Learn more about asymptote  brainly.com/question/10730051
  2. Learn more about logarithmic function brainly.com/question/1447265
  3. Learn more about the graph of this logarithmic function brainly.com/question/9132850

<h3>Answer details</h3>

Grade:  9

Subject:  mathematics

Chapter:  logarithmic function

Keywords:  logarithmic function, asymptote, graph, curve,  the inverse function

You might be interested in
Which one is greater 16,400 or 1.64 times 10 to the 4th power.<br> Sorry it is confusing.
Kitty [74]

Answer: its the same amount

Step-by-step explanation:

8 0
2 years ago
melissa can earn $18 each time she cuts grass. if she cuts the grass x times, write an expression that shows how much she will e
Alborosie

18x

Simple as that. 18 times however many times she cuts the grass

7 0
2 years ago
Which are correct statements regarding proofs? Select three options.
kompoz [17]

Answer:

In a paragraph proof, statements and their justifications are written in sentences in a logical order.

A two-column proof consists of a list statements and the reasons the statements are true.

A paragraph proof is a two-column proof in sentence form.

Step-by-step explanation:

  • In a paragraph proof, statements and their justifications are written in sentences in a logical order.
  • A two-column proof consists of a list statements and the reasons the statements are true.
  • A paragraph proof is a two-column proof in sentence form.

A paragraph proof is only a two-column proof written in sentences. However, since it is easier to leave steps out when writing a paragraph proof.

A two-column geometric proof consists of a list of statements, and the reasons that we know those statements are true. The statements are listed in a column on the left, and the reasons for which the statements can be made are listed in the right column

8 0
2 years ago
A sector with a radius of 8 cm has an area of 56pi cm2. What is the central angle measure of the sector in radians?
Maurinko [17]

Answer:

\frac{7\pi}{4}.

Step-by-step explanation:

Given information:

Radius of circle = 8 cm

Area of sector = 56\pi\text{ cm}^2

Formula for area of sector is

A=\dfrac{1}{2}\theta r^2

where, r is radius and \theta is central angle in radian.

Substitute A=56\pi and r=8 in the above formula.

56\pi=\dfrac{1}{2}\theta (8)^2

56\pi=\dfrac{64}{2}\theta

56\pi=32\theta

\dfrac{56\pi}{32}=\theta

\dfrac{7\pi}{4}=\theta

Therefore, the measure of the sector in radians is \frac{7\pi}{4}.

6 0
2 years ago
What is the answer i'm having trouble :( click the picture
Vikentia [17]

Step-by-step explanation:

So 2 pints = 1 quart

She need 3 quart

so 2 pints × 3 = 1 quart × 3

6 pints = 3 quart

...

The she need 6 pints which is

2 cups = 1 pint

She need 6, so mutiply with 6

2 cups × 6 = 1 pint × 6

12 cups = 6 pints

Then this is the answer, you got

12 cups = 6 pints = 3 quart

She need 12 cups of water to make fruit punch

5 0
2 years ago
Other questions:
  • How to solve this problem I️ need help I️ am very confused
    12·1 answer
  • HELP ME OUT PLEASE!!
    12·1 answer
  • How to solve inequalities with word problems
    15·1 answer
  • A trapezoid is quadrilateral with at least one pair of parallel sides. The quadrilateral shown is a trapezoid. If m&lt;1 = 90* a
    13·1 answer
  • The local business will donate $5.00 for every 10 tickets
    7·1 answer
  • Bivariate data is data for two, usually related, variables. Each value of one variable is paired with a value of the other, for
    6·1 answer
  • Jamal has at most $100 to spend on computer paper and printer ink for his computer. He buys 1 box of paper for $24.99. If ink ca
    13·1 answer
  • 10 points!! Can yo7 say the answer and explain it I will give brainleest
    5·1 answer
  • Help please!!!,,,,,,
    8·1 answer
  • Solve (x + y +2)(y + 1)
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!