Graph the rational function f(x)=(3x-1)/(x-5)
To graph the rational function f(x) = (3x - 1) / (x - 5), follow these steps. Find the vertical asymptote(s) by setting the denominator equal to zero and solving for x.
x - 5 = 0
x = 5
The vertical asymptote of the function is x = 5.
Step 1: Find the horizontal asymptote by comparing the degrees of the numerator and denominator polynomials. Since the degree of the numerator (3x - 1) is 1, and the degree of the denominator (x - 5) is also 1, the horizontal asymptote is given by the ratio of the leading coefficients:
Horizontal asymptote: y = 3/1
Horizontal asymptote: y = 3
Step 2: Find the x-intercept by setting the numerator equal to zero and solving for x:
3x - 1 = 0
3x = 1
x = 1/3
The x-intercept is (1/3, 0).
Step 3: Find the y-intercept by setting x to zero and evaluating the function:
f(0) = (3 * 0 - 1) / (0 - 5)
f(0) = -1 / -5
f(0) = 1/5
The y-intercept is (0, 1/5).
Step 4: Find additional points to sketch the graph. Choose some x-values around the vertical asymptote (x = 5) and calculate the corresponding y-values. For example, you can use x = 4, x = 6, and x = 8.
x = 4:
f(4) = (3 * 4 - 1) / (4 - 5)
= 11 / -1
= -11
x = 6:
f(6) = (3 * 6 - 1) / (6 - 5)
= 17 / 1
= 17
x = 8:
f(8) = (3 * 8 - 1) / (8 - 5)
= 23 / 3
≈ 7.67
Step 5: Plot the points obtained from Steps 2 to 5 and draw the graph. The graph should approach the horizontal asymptote (y = 3) as it approaches the vertical asymptote (x = 5).
The graph of the rational function f(x) = (3x - 1) / (x - 5) should look like this:
To know more about rational function :
https://brainly.com/question/13671639
#SPJ2
30 POINTS FOR THIS...Bus Stop: A graph has time (minutes) on the x-axis, and distance (miles) on the y-axis. A line goes through points (0, 5), (6, 8), and (12, 11). Friend's house: A 2-column table with 3 rows. Column 1 is labeled Time (minutes) with entries 3, 6, 9. Column 2 is labeled Distance (miles) with entries 4, 6, 8.
Seth is comparing scenarios to determine which starting point he should get dropped off at to get him to school faster. Seth's house is 17 miles from school.
In which scenario does Seth start closer to school?
In which scenario does Seth travel at a greater speed, and what was the rate?
Answer:
In which scenario does Seth start closer to school?
bus stop, 5 miles from home
In which scenario does Seth travel at a greater speed, and what was the rate?
friend’s house, 2 miles every 3 minutes
The speed of Seth when he travels from the Bus stop will be faster. Because the speed is greater.
What is an average speed?The distance covered by the particle or the body in an hour is called the average speed. It is a scalar quantity. It is the ratio of the total distance to the total time.
We know that the average speed formula is given as,
Average speed = Total distance / Total time
The speed of Seth when he travels from the Bus stop will be
Average speed = (8 - 5) / (6 - 0)
Average speed = 3 / 6
Average speed = 0.5 miles per hour
The speed at Seth when he travels from the Friend's house will be
Average speed = (8 - 4) / (9 - 3)
Average speed = 4 / 6
Average speed = 0.33 miles per hour
The speed of Seth when he travels from the Bus stop will be faster. Because the speed is greater.
More about the average speed link is given below.
https://brainly.com/question/12322912
#SPJ2
For homework. I can't understand how to do this
What is the benefit of writing expressions to represent real-world situations?
Answer: it help understand life better
Step-by-step explanation:
Is the equationy=-1/2 linear or nonlinear?
Answer:
y = -1/2 is a horizontal line; a line with no slope. With that said, it is linear.
Step-by-step explanation:
Can you pls help me with these questions?
I'm giving brainliest ^^
Answer:
A. 15, 9, 3, -3, -9
Step-by-step explanation:
That's all I know, sorry
Answer:
See attached pdf
Step-by-step explanation:
At Supply World, 4 pens cost $10.00. How much do 3 pens cost if the price per pen is the same?
Answer:
$7.50
Step-by-step explanation:
Help me please.........
hey can someone help me with that
Answer:
70
Step-by-step explanation:
because it stand itself
Answer:
The answer is 280
Step-by-step explanation:
400/100=4, so must multiply 70 x 4 = 280
Determine how far the vehicle travels in 3 hours. A ferry travels 45 miles every 1 1/2 hours.
Answer:
Um 90 miles lol
Step-by-step explanation:
Need help on
These 2 questions
Answer:
so the answer to the bottom problem is 69
hope this helped i use desmos scientific counculator
- the chair with internet
What is the slope of the line that passes through the points (-8, -3)(−8,−3) and (-12, -3) ?(−12,−3)? Write your answer in the simplest form.
Answer:
(-3,-5) is the answer
Answer:
-3
Step-by-step explanation:
true or false:
1. 7 = (-5) - (-12)
2.The difference between -5 and -12 is equal to (-5) - (-12)
3.The difference between -12 and -5 is equal to (-5) - (-12)
4.(-5) + 12 = (-5) - (-12)
5.(-5) + (-12) = (-5) - (-12)
Answer:
1. True
2. False
3. False
4. True
5. False
Step-by-step explanation:
1. 7 = (-5) - (-12)
7 = -5 + 12
7 = 7
2. -5 - 12 = -17
-5 - (-12) = 7
3. -12 - 5 = -17
-5 - (-12) = 7
4. 7 = 7
5. -17 = 7
What value of w makes the equation 145 = w + 27 true?
Answer:
118
Step-by-step explanation:
In the equation 145 = w + 27, you can solve for w by subtracting 27 from 145. That would give you 118. You can check this is correct by adding 27 to 118. 118 plus 27 = 145.
Answer:
118
Step-by-step explanation:
145 = w + 27
Switch the + sign before the 27 and switch into a minus and move it to the other side.
145-27=w
145-27=118
w=118
The ratio of blue marbles to red marbles in a box is 3 to 2. if there are 12 blue marbles in a box then how many red marbles are there?
Answer:
8 red marbles.
Step-by-step explanation:
The ratio is 3:2, blue to red. If there's 12 blue marbles and the first part of the ratio's 3, then:
12/3=4
Then you take the 4 and multiply it by 2, the second half of the ration to get 8.
And so, the answer's 8. If you divide 12:8 by 4 each you get your original ratio of 3:2, so that's your way to check.
Which rate has the same unit rate as 8 books in 12 weeks?
F. 2 books in 1 week H. 6 books in 15 weeks
G. 5 books in 7 weeks J. 3 books in 4.5 weeks
Answer: 3 books in 4.5 weeks
Step-by-step explanation:
Answer:
3 books in 4.5 weeks
Step-by-step explanation:
23,461 rounded to the nearest hundred
Answer:
23,500
Step-by-step explanation:
Pls help me! this is a long overdue assignment! (question is in the picture)
Answer:
three basic methods of graphing linear functions.
The first is by plotting points and then drawing a line through the points.
The second is by using the y-intercept and slope.
The third is applying transformations to the identity function f(x)=x.
The Boardman family walked two over five of a mile in two over seven of an hour. What is their unit rate in miles per hour?
two-sevenths over two-fifths equals one and two-fifths miles per hour
two-sevenths over two-fifths equals five over seven miles per hour
two-fifths over two-sevenths equals one and two-fifths miles per hour
two-fifths over two-sevenths equals five over seven miles per hour
Answer:
two-fifths over two-sevenths equals one and two-fifths miles per hour .
Sami purchased 5 comic books priced as shown.
$4.50 $3.75 $3.95 $2.19 $3.24
If sales tax is 9%, what is the total price Sami paid? Round to the nearest cent, if necessary.
Answer:
$19.23
Step-by-step explanation:
First, add the prices of all 5 comics together. That should equal $17.63. The tax is 9% so that would be 1.5867 or $1.60. In total, Sami paid $19.23.
please help. I really need it.
if you get right you get brainliest :D
Answer:
A
Step-by-step explanation:
Because a negative minus a negative is the same as adding the two together :)
Answer:
8.5
Step-by-step explanation:
The opposite of -8 is 8.
\frac{1}{2}+8
Convert 8 to fraction \frac{16}{2}.
\frac{1}{2}+\frac{16}{2}
Since \frac{1}{2} and \frac{16}{2} have the same denominator, add them by adding their numerators.
\frac{1+16}{2}
Add 1 and 16 to get 17.
\frac{17}{2}
Plsss helppp i rlly need help with this math!!!
Answer:
13.150
14. 11.2
Step-by-step explanation:
Have a good day :)
"Determine if the following argument allways aplies sometimes or never provide atleast 2 examples "To convert yards to feet, devide the number of yards by 3" ANSWER ASAP.
Answer:
It does not apply because if you divide say 3 yards by 3 you would get 1 not 9. You have to multiply the yards by three not divide.
Step-by-step explanation:
A circular swimming pool measures 79 feet around. What is the diameter?
A. about 200 ft
B. about 25 ft
C. about 50 ft
D. about 100 ft
Answer:
B. about 25 ft
Step-by-step explanation:
you have to add the numbers up a 4 tiems then your awnser comes in and if not multiply 79 2 times your welcome
Step-by-step explanation:
Select the three true statements.
1. pi is the area of a circle of radius 1.
2. pi is the area of a circle of diameter 1.
3. pi is the circumference of a circle of radius 1.
4. pi is the circumference of a circle of diameter 1.
5. pi is the constant of proportionality relating the diameter of a circle to its circumference.
6. pi is the constant of proportionality relating the radius of a circle to its area.
Answer:
9/2
Step-by-step explanation:
this is a khan academy question
Answer:
Its A hope this is correct, please give me brainliest, my dog died today :(
Step-by-step explanation:
what is the answer to 2x+3y=-13
Answer:
solve for x
x=(-13/2-3y/2
solve for y
y= -13/2-2x/3
Step-by-step explanation:
hope its the answer you where looking for
you dont have to do all of them but if u do u get 5 stars and brainiest but pls help mee
Answer:
1)m=-6 2)p=-25 3)n=13 4)x=1 5)n=-18 6)r=46 7)=-17 8)x=-30 9)n=49 10)a=33
Step-by-step explanation:
Which of the following expressions represents the phrase "six added to five times a number"?
O6+5x
O6+5+x
O5+6x
o 11 x