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
BigorU [14]
3 years ago
9

F(x)= x-2/ x-4

Mathematics
1 answer:
hodyreva [135]3 years ago
6 0

Answer:

The discontinuity is x = 4

There no holes

The equation of the vertical asymptote is x = 4

The x intercept is 2

The equation of the horizontal asymptote is y = 1

Step-by-step explanation:

* Lets explain the problem

∵ f(x)=\frac{x-2}{x-4}

- To find the point of discontinuity put the denominator = 0 and find

 the value of x

∵ The denominator is x - 4

∵ x - 4 = 0 ⇒ add 4 to both sides

∴ x = 4

* The discontinuity is x = 4

- A hole occurs when a number is both a zero of the numerator

 and denominator

∵ The numerator is x - 2

∵ x - 2 = 0 ⇒ add 2 to both sides

∴ x = 2

∵ The denominator is x - 4

∵ x - 4 = 0 ⇒ add 4 to both sides

∴ x = 4

∵ There is no common number makes the numerator and denominator

   equal to 0

∴ There no holes

- Vertical asymptotes are vertical lines which correspond to the zeroes  

  of the denominator of the function

∵ The zero of the denominator is x = 4

∴ The equation of the vertical asymptote is x = 4

- x- intercept is the values of x which make f(x) = 0, means the

 intersection points between the graph and the x-axis

∵ f(x) = 0

∴ \frac{x-2}{x-4}=0 ⇒ by using cross multiplication

∴ x - 2 = 0 ⇒ add 2 to both sides

∴ x = 2

* The x intercept is 2

- If the highest power of the numerator = the highest power of the

 denominator, then the equation of the horizontal asymptote is

 y = The leading coeff. of numerator/leading coeff. of denominator

∵ The numerator is x - 2

∵ The denominator is x - 4

∵ The leading coefficient of the numerator is 1

∵ The leading coefficient of the denominator is 1

∴ y = 1/1 = 1

* The equation of the horizontal asymptote is y = 1

You might be interested in
The slope of the line whose equation is 3 y = 2 x - 3 is
fiasKO [112]
The photo has the answe

6 0
3 years ago
mr george has a bank balance of 42 dollar at the start of the mouth.after he depostite 6 dollar the new balance is
Lubov Fominskaja [6]

Answer:

48 dollars.

Step-by-step explanation:

If Mr. George starts with 42, and adds 6, his new balance should equal 48 because you add the two numbers.

7 0
3 years ago
Read 2 more answers
HELPP!!what is the answer to this picture above^
nasty-shy [4]

Answer:

\fbox{ \fbox { \sf{Distance  =  \sf{15 \: units}}}}

{ \fbox { \fbox { \sf{Midpoint = { \sf{ \: (12 \: , \: 10.5)}}}}}}

Step-by-step explanation:

\star{ \:  \sf { \: Let \: the \: points \: be \: A \: and \: B}}

\star { \sf{Let \: A(6 \:, 6) \: be \: (x1 ,\: y1) \: and \: B(18 ,\: 15) \: be \: (x2 \:, y2)}}

\underline{ \underline{ \tt{Finding \: the \: distance}}}

\boxed{ \sf{Distance =  \sqrt{ {(x2 - x1)}^{2}  +  {(y2 - y1)}^{2} } }}

\mapsto{ \sf{Distance =  \sqrt{ {(18 - 6)}^{2}  +  {(15 - 6)}^{2} } }}

\mapsto{ \sf{Distance =  \sqrt{ {(12)}^{2}  +  {(9)}^{2} } }}

\mapsto{ \sf{Distance =  \sqrt{144 + 81}}}

\mapsto{ \sf{Distance =  \sqrt{225} }}

\mapsto{ \sf{Distance =  \sqrt{ {15}^{2} } }}

\mapsto{  \boxed{\sf{Distance = 15 \: units}}}

\underline{ \underline {\tt{Finding \: the \: Midpoint}}}

\boxed{ \sf{Midpoint = ( \frac{x1 + x2}{2}  \: , \:  \frac{y1 + y2}{2} )}}

\mapsto{ \sf{Midpoint = ( \frac{6 + 18}{2}  \: , \:  \frac{6 + 15}{2} )}}

\mapsto{ \sf{Midpoint = ( \frac{24}{2}  \: , \:  \frac{21}{2} )}}

\mapsto{ \boxed{ \sf{Midpoint = (12 \: , \: 10.5)}}}

Hope I helped!

Best regards! :D

~\sf{TheAnimeGirl}

3 0
3 years ago
Whats the square root of 25ab^6
r-ruslan [8.4K]
5b^3 sq rt of a

There's not enough a's
7 0
3 years ago
Read 2 more answers
IN A SHOP THE NORMAL PRICE OF A JACKET IS $60 . THE COST OF THE JACKET IN A SALE IS 3 BY 4 OF THE NORMAL PRICE
kramer

Answer:

$45

Step-by-step explanation:

3/4×60= 45

cost of jacket in sale: $45

hope it helps!

5 0
3 years ago
Other questions:
  • Solve this expression 5(4x-13).
    15·2 answers
  • What does it mean when a line of best fit has a correlation coefficient close to 0?
    10·1 answer
  • A.
    7·1 answer
  • X2 + 12x =<br> – 20<br> what are the roots of the following quadratic equation
    15·1 answer
  • The cost of carpeting a square yard is $8.60. How much does it cost to carpet 9.7 square yards?
    12·1 answer
  • 7+(8+4) order of operations
    9·2 answers
  • PLSSSSSSSS HELP ME <br> correct answer gets brainliest
    6·1 answer
  • A bookkeeper needs to post the cost of the desk and the chair into his records. The cost of the desk is fives times the cost if
    15·1 answer
  • HELP PLEASE!!!
    9·1 answer
  • Write the equation of the line that passes through the given points. (0,-1) and (-11,-4)
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!