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]
2 years ago
9

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

Mathematics
1 answer:
hodyreva [135]2 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
Simplifly the expression 5^0
Angelina_Jolie [31]

ANY number raised to the zero power is ' 1 '.

(This rule is worth memorizing.  You'll amaze all of
your friends, especially the ones who don't know
how to do it without running to Google.)

So  5^0  =  1 .

3 0
2 years ago
The number 1.3,1/1/3,1.34 in least to greatest
elixir [45]
1.3, 1 1/3, 1.34

The decimal version of 1 1/3 is 1.333 (so on)

so 1.3 is less than 1.333 and 1.333 is less than 1.34

1.3<1.333<1.34
4 0
3 years ago
A car rental costs $32 as a base fee, plus $28 per day. Use the explicit rule f (n )= 28n + 32
alexdok [17]

Answer:

The charges paid for the first four days are:

  • <u>$144</u>.

Step-by-step explanation:

To obtain the charges paid for the first 4 days, you must use the given explicit rule given:

  • f (n) = 28n + 32

Where:

  • <em>n = Number of days the person rents the car.</em>

As we need to obtain the charges to 4 days, we replace this value in the explicit rule:

  • f (n) = 28n + 32
  • f (4) = 28(4) + 32
  • f (4) = 112 + 32
  • <u>f (4) = 144</u>

With these calculations, <u>you can identify the charges paid for the first 4 days are $144</u>, <em>where $112 is the money by each day of the four days and $32 is the base fee</em>.

3 0
3 years ago
If Clarie bikes at an average speed of 7
Reika [66]

Answer: 4

Step-by-step explanation:

7 0
2 years ago
Which of the following is a proportion?
poizon [28]

Answer:

Option C, 14/21=9/21 is the proportion.

Step-by-step explanation:

Given:

a.5/7 = 10/12

b.9/15 = 12/18

c.4/6 = 8/12

d.14/21 = 9/12

We have to find the proportions.

In proportion two ratios are equal, as it has an equality sign in between so both side must be of same ratio in its simplest form.

Let's work with option C

⇒ \frac{4}{6}=\frac{8}{12}

To find the simplest form we have to divide the numerator and denominator with same digit (or its factor).

Simplest form of  \frac{8/2}{12/2} = \frac{4}{6} , \frac{4/2}{6/2}= \frac{2}{3}

Simplest form of \frac{4}{6} = \frac{2}{3}

Both sides in option C have equal ratios of 2/3.

So 4/6=8/12 is in proportion.

6 0
3 years ago
Other questions:
  • A medical school claims that more than 28% of its students plan to go into general practice. It is found that among a random sam
    10·2 answers
  • Solve the inequality. 6y+5&gt;8
    9·2 answers
  • Sum of ten and the quotient of a number x and 6
    10·2 answers
  • 48x2 + 48xy2 + 12y4 =
    5·2 answers
  • 2 liters of orange juice and 1.5 liters of applejuice
    11·1 answer
  • The triangles shown are congruent.
    7·2 answers
  • What is the vertex of the quadratic function f(x)=(x-6)(x2)
    6·1 answer
  • Can anybody help me on this
    11·2 answers
  • Lauren drew a tower using only similar quadrilaterals.
    10·2 answers
  • PLZ HELP! <br><br> Add.<br><br> −16 + (−29) + 49 = <br><br><br> 4<br><br> 62<br><br> 94
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!