Which function has a graph with a vertical
asymptote at x = 7 and a horizontal asymptote at
f(x) = -3?
Please help me
Answers
Answer:
[tex]f(x)=\frac{1}{x-7}-3[/tex], see the graph attached for a visual reference.
Step-by-step explanation:
Vertical asymptotes are only present in rational functions where the parent function [tex]f(x)=\frac{1}{x}[/tex] has a vertical asymptote at the line [tex]x=0[/tex] and a horizontal asymptote at the line [tex]y=0[/tex]. Because the vertical asymptote has to be [tex]x=7[/tex], the denominator must be x-7 in order for the denominator to equal 0. For the horizontal asymptote to be [tex]y=-3[/tex], then 3 must be subtracted from the rational function. Therefore, the function that has these asymptotes is [tex]f(x)=\frac{1}{x-7}-3[/tex].
To find the vertical asymptotes, set the denominator of f(x) equal to zero.
-3x - 3 = 0
-3x = 3
x = -1
The vertical asymptote is
x = -1
To find the horizontal asymptotes, we examine the degree of the numerator and denominator of f(x). We use the leading terms to determine the degree. The leading term in the numerator is 7x0. The leading term of the denominator is -3x1. Since the exponent of x in the numerator is 0, the degree is 0 . Since the exponent of x in the denominator is 1, the degree is 1. The degree in the numerator is less than the degree in the denominator. Therefore, the horizontal asymptote is
y = 0
This also indicates that there are no x-intercepts.
To find the y-intercepts, set x=0.
The y-intercept is (0, -7/3).
Related Questions
For the past ten years, Michelle has been tracking the average annual rainfall in Boynton Beach, Florida by recording her data in the given table. She has concluded that the relationship can be modeled by a linear function.
Year 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
Average Rainfall(in inches) 62.33 61.8 61.27 60.74 60.21 59.68 59.15 58.62 58.09 57.56
Use the values provided in the table to create a linear graph of the data. On the graph, let x = 0 represent the year 2004. Be sure to include all proper labels on the graph.
Answers
55.44 inches
Step-By-Step Explanation
part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.
slope = m = (change in rainfall)/(change in years)
= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53
then the point-slope form of the equation of the line can be written as
y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)
y = -0.53x +62.33 . . . x = years after 2004
part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is
y = -0.53·13 +62.33 = 55.44 . . inches
the predicted rainfall in 2017 is 55.44 inches.
The linear equation that represents the table is [tex]y = -0.53x + 62.33[/tex]
What are linear functions?A linear function is a graph that has a constant rate.
From the table, we have the following ordered pairs
(x,y) = (0,62.33) and (1, 61.8)
Start by calculating the slope (m)
[tex]m = \frac{y_2 -y_1}{x_2-x_1}[/tex]
So, we have:
[tex]m = \frac{61.8 -62.33}{1-0}[/tex]
[tex]m = -0.53[/tex]
The linear equation is then calculated as:
[tex]y = m(x -x_1) + y_1[/tex]
So, we have:
[tex]y = -0.53(x -0) + 62.33[/tex]
Expand
[tex]y = -0.53x + 62.33[/tex]
Hence, the linear equation that represents the table is [tex]y = -0.53x + 62.33[/tex]
Read more about linear equations at:
https://brainly.com/question/14323743
A rectangle as shown has a length of 0.9 centimeters and a width of 0.4 cm. A circle is drawn inside that touches the rectangle at two points.
What is the area to the shaded region in the rectangle.
Answers
Answer:
it should be 0.23 cm when rounded to the nearest hundredth
The ratio of red to blue to pink marbles is 11:8:5. If there are 40 total blues, how many
marbles are there altogether?
A. 25
B. 40
C. 55
D. 120
Answers
Answer:
D) 120
Step-by-step explanation:
if there are 40 blue marbles and the ratio of blue is 8, then the multiplier is 5
# of red marbles: 11 x 5 = 55
# of pink marbles: 5 x 5 = 25
55 + 40 + 25 = 120
I WILL REWARD BRAINLIEST
Which shows a statistical question regarding a data set?
What is the total number of ounces in a pound?
What is the total number of wheels on a tricycle?
What is the total number of ounces in a pint-size container?
What is the total number of students who brought water bottles to lunch?
Answers
Answer:
What is the total number of students who brought water bottles to lunch?
Step-by-step explanation:
Answer:
What is the total number of students who brought water bottles to lunch?
Step-by-step explanation:
Giving Brainly For Correct Answer
Chandra had scores of 100, 70, and 85 on three of her five tests. She cannot remember her two other scores, which were both the same. She does remember that the mean of the five scores is 75. Which statement below explains how to find the two missing scores?
Add the sum of the three test scores to the product of 75 and 5.
Subtract the sum of the three test scores from the product of 75 and 5.
Add the sum of the three test scores to the product of 75 and 5, and then double the result.
Subtract the sum of the three test scores from the product of 75 and 5, and then divide the result by 2.
Answers
I think
Answer:
Subtract the sum of the three test scores from the product of 75 and 5, and then divide the result by 2.
Step-by-step explanation:
From the question:
100, 70, 85 on three of her five tests
Total number of test = 5
mean of the five scores is 75
mean = average of the five scores
Average score = Total score / total number of test
Total score = Average score * total number of test
= 75*5 =375
to find remaining two tests' scores
Total score - the 3 scores from question
= 375 - 100 - 70 - 85
=120
If u want to find the score of each of the unknown test
From question:
She could not remember the other two scores, which were the same.
Thus,
The score of one test
= 120/ 2
=60
giving/rewarding brainly for correct answer
Answers
Answer:
8516 meters
Step-by-step explanation:
So the closest answer is 8485
The sum of two numbers is 80. If the difference between the same two numbers is 8, find the two numbers.
Answers
Answer:
The numbers are 44 and 36
Step-by-step explanation:
n + n - 8 = 80
2n - 8 = 80
2n (- 8 + 8) = 80 + 8
2n = 88
2n/2 = 88/2
n = 44
44 - 8 = 36
What is the value of Z ?
Answers
Answer:
z=130°
Step-by-step explanation:
These are supplementary angles so
z=180-50=130°
Answer:
130
Step-by-step explanation:
That is a straight angle. It has 180 degrees, correct? So you'd have to subtract 180-50 to get your answer of 130.
Please help me with this:)
Answers
plug in the points into the formula:
(-3-2)^2 + (-1-5)^2 whole thing is square rooted
(-5)^2 + (-6)^2 whole thing square rooted
(25) + (36) whole thing square rooted
square root of 61 -> the second choice is correct !
What is the surface area of each figure? Round to the nearest tenth if necessary.
Answers
Answer:
where is the figure....
l think there is smthng wrong...
A tree in Kevin's backyard is 5/8 meters tall. It has been growing for 1 2/5 years. What is the unit rate in meters per year? No links.
Thank you.
Answers
Answer:
o.4464287142 or 0.4
Step-by-step explanation:
The tree is 5/8 meters tall and that's in 1 2/5 years so you would divide them and you get .4464287142
Line segments AB and CD intersect at point E. Ray EF extends from point E.
Find the value of x. Then find the measures of angles CEF and BEF
Answers
Answer:
x=29 CEF=103 BEF=58
Step-by-step explanation:
161=3x+16+2x
5x=145
x=29
please help and all you can 1 to 9
Answers
Two lines intersect at a point that is also a vertex of an angle.
Write and solve equations to determine the values of x and y
Answers
Answer are that y and x are 34.5.
20 points (If you answer to just get points i will remove you from this sight)
30:40 = 35:?
Answers
Answer:
[tex] \frac{30}{40} = \frac{35}{x} [/tex]
[tex] \frac{3}{4} = \frac{35}{x} [/tex]
[tex]3x = 140[/tex]
[tex]x = 46 \frac{2}{3} [/tex]
A recipe for 60 cookies calls for 1 pound of butter. How much butter is needed to make 2 dozen cookies? Write answer as a fraction using /, or decimal.
Answers
Answer:0.4 lbs of butter
Step-by-step explanation:
60/12 is 5
That is how many dozens that use 1 pound of butter
Then 1/5 is 0.2
That is how much pounds of butter is in one dozen
0.2*2 is 0.4
That is two dozens
all you have to do is say what time it is and it’s also inverted
Answers
Answer:
Step-by-step explanation:
Answer:
9.15
Step-by-step explanation:
the first one is nine fifteen
(Middle school math) I just need to know the probabilities for letter a. Thank you.
Answers
Answer:
use a tree diagram to get a visual representation over it then calculate you're probability.
16 + 36 Drag numbers to the lines to create an equivalent expression in factored form
Answers
52
this is most likely the correct answer
52
Step-by-step explanation:
NEED HELP FASTT!
Jayden is trying to find the volume of his closet to see how much can fit inside. If the area of the floor is 14 square feet, and the closet is 612 feet tall, what is the volume in cubic feet?
Answers
u already have one step done, which is the area, bc the formula for volume is length x width x height, and area is length x width, so u just have to multiply it by the height
Armando is going
to replace the trim
around all of the doors in his house. The
outside of each door measures 18 feet
.
If he has 9 doors, how many inches of
,
trim does he need to replace?
Answers
add 223+374+402 using expanded form
next,change your answer back too standard form
Answers
the answer is 999
or 900 90 9
hope this helps have a good day
And the is 999
What is the total weight in ounces of the three heaviest boxes?
Please help me worth branliest chart and answer choices on picture tysm if u help
Answers
Answer:
D. 252 ounces
Step-by-step explanation:
The number line is cut in fourths. The 3 heaviest boxes are, 1 between 4 and 5 lbs, and 2 boxes between 5 and 6.
1st box: 4.75 lbs
2nd box: 5.5 lbs
3rd box: 5.5 lbs
Total lbs: 15.75 lbs
15.75 pounds= 252 ounces
***** NO LINKS******
Answers
Answer:
1 inch = 80 miles
Step-by-step explanation:
4 and three quarters = 4.75
380 divided by 4.75 = 80
Double check and multiply 4.75x80
4.75 x 80 = 380
Which of the following would form a triangle with the two existing sides of 3 inches and 5 inches
Answers
is there photos for this question? sorry im a lil confused on "what the following" are
Which value of x makes the equation true?
−4=1.5x+5
Answers
Answer:
For x = -6
Step-by-step explanation:
1.5x + 5 = -4
1.5x = -4 - 5
1.5x = -9
x = -6
Checking: 1.5 * -6 + 5 = -4
1. You subtract 5 to both sides
2. divide 1.5 to the other number
how to solve multi-step inequalities?
Answers
Someone help me with this please
Answers
for question 1
Area of Base B =45×25 = 1125 cm²
perimeter of base P = 2(45+25) = 140 cm
Height = 15 cm
Using the formula
Surface area = 2B + Ph
A = 2×1125 + 140×15= 4350 cm²
Voume = Bh = 1125×15= 16875 cm³
For question 2,
Area of base = 7× 5/2= 17.5 cm²
Perimeter of base = (7+7+7) = 21 cm
Surface area = 2B + Ph
Surface area of prism = 2×17.5+ 21×10 = 245cm²
Volume = Bh = 17.5×10 = 175 cm³
Answer:
Step-by-step explanation:
for question 1
Area of Base B =45×25 = 1125 cm²
perimeter of base P = 2(45+25) = 140 cm
Height = 15 cm
Using the formula
Surface area = 2B + Ph
A = 2×1125 + 140×15= 4350 cm²
Voume = Bh = 1125×15= 16875 cm³
For question 2,
Area of base = 7× 5/2= 17.5 cm²
Perimeter of base = (7+7+7) = 21 cm
Surface area = 2B + Ph
Surface area of prism = 2×17.5+ 21×10 = 245cm²
Volume = Bh = 17.5×10 = 175 cm³
Can I get some help please?
Answers
Answer: A
Step-by-step explanation:
A linear function is described as:
https://tex.z-dn.net/?f=f(x)%20%3D%20ax%20%2B%20b
When the value of x = 0, then you're left with
https://tex.z-dn.net/?f=f(x)%20%3D%20b
In this question, the speed of sound is the linear function while the temperature is the independent variable. When T = 0, you're left with
https://tex.z-dn.net/?f=S(0)%20%3D%20331.4
Which means the speed of sound in air when temperature is 0°C is 331.4m/s.
Please help me I am so confused