Which graph represents the function f(x)=1/x+3-2
Answers
files are attached below
Answer:
The graph as shown below.
Step-by-step explanation:
Given : The function [tex]f(x)=\frac{1}{x-3}-2[/tex]
We have to plot the graph for the given function [tex]f(x)=\frac{1}{x-3}-2[/tex]
Consider the given function [tex]f(x)=\frac{1}{x-3}-2[/tex]
Domain of function [tex]f(x)=\frac{1}{x-3}-2[/tex]
DOMAIN is set of input values for which the function is real and has defined values.
So, The given function is undefined at x = 3
So, Domain is [tex]x<3\quad \mathrm{or}\quad \:x>3[/tex]
RANGE is the set of values of dependent variable for which the function is defined.
Inverse of given function is [tex]y=\frac{3x+7}{x+2}[/tex]
Now, domain of inverse function is [tex]f\left(x\right)<-2\quad \mathrm{or}\quad \:f\left(x\right)>-2[/tex]
Now, x intercept and y- intercepts
x intercept where y = 0 and y- intercept where x= 0
Let f(x) = y
Then [tex]y=\frac{1}{x-3}-2[/tex]
Put x = 0
thus y- intercept is [tex]\left(0,\:-\frac{7}{3}\right)[/tex]
Now put y = 0
Then x- intercept is [tex]\left(\frac{7}{2},\:0\right)[/tex]
Now, Calculate the vertical and horizontal asymptotes,
Vertical asymptotes,
Go over every undefined point and check if at least one of the following statements is satisfied.
[tex]\lim _{x\to a^-}f\left(x\right)=\pm \infty[/tex]
[tex]\lim _{x\to a^+}f\left(x\right)=\pm \infty[/tex]
Thus, The vertical asymptotes is x = 3
And For horizontal asymptotes,
[tex]\mathrm{Check\:if\:at\:}x\to \pm \infty \mathrm{\:the\:function\:}y=\frac{1}{x-3}-2\mathrm{\:behaves\:as\:a\:line,\:}y=mx+b[/tex]
We have y = -2 as horizontal asymptotes.
Plot we get the graph as shown below.
Related Questions
A math club took a test. Twelve of the members had an average score of 80. Eighteen of the members had an average score of 86.
what was the class average score?
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hope tis helps
y equals x + z + 5 Z equals -3 y - 3 2x minus y equals negative 4 How can i solve using 3 variable systems of equation
Answers
If you have
x +z +5z = -3y -3
3x -y = -4
Then you can rewrite as
x = -1.5 -0.6z
y = -0.5 -1.8z
_____
You can get this by any of the usual methods of solving linear equations. Just treat the system as two equations in x and y with the z terms on the right side of the equal sign:
x +3y = -3 -6z
3x -y = -4
Simplify the expression. (x1/8 y1/4)2
Answers
Answer:
Step-by-step explanation:
C) x1/4y1/2
hey can you please help me posted picture of question
Answers
Explanation:
Multiply all the items to get all the possible outcomes (in this case sandwiches).
Kinds of breads = 3
Kinds of meat = 4
Kinds of cheese = 3
Hence 4*3*3 = 36 (Option D)
Use complete sentences to describe the domain of the cosine function.
Answers
The cosine function takes x values from all real numbers.
Therefore, the domain of the cosine function is a real numbers.
im posting several questions i need help with in an image
Answers
(1) n = 4
(2) x = 30
(3) a = -4
(4) n =10
(5) n = -46.2
Explanation:
(1) Given
9n-8 = 28
9n = 28 + 8
9n = 36
n=4
(2) Given
-1-x = -31
-x = -31 + 1
x = +31 - 1
x = 30
(3) Given
9-4a = -5a + 5
-4a + 5a = 5 - 9
a = -4
(4) Given
n/2 = 5
n=5*2
n = 10
(5) Given
29.5 = -16.7 -n
n = -16.7 - 29.5
n = -46.2
9n = 28 + 89n = 36n=4
2.
-x = -31 + 1x = 31 - 1x = 30
3.
9-4a = -5a + 5-4a + 5a = 5 - 9
a = -4
4.
n/2 = 5n=5*2 n =10
5.
29.5 = -16.7 -nn = -16.7 - 29.5n = -46.2
A = LW ; for L whats the answer step by step
Answers
_________________________________________________
Explanation:
_________________________________________________
Given:
_________________________________________________
" A = LW " ; Solve for "L" ; {step-by step} ;
_________________________________________________
A = L * W ;
↔ L * W = A ;
Divide each side of the equation by "W" ;
to isolate "L" on one side of the equation; & to solve for "L" ;
→ { L * W } / L = A / L ;
to get:
→ W = L / A .
________________________________________________________
The answer is: " W = L / A " .
________________________________________________________
the cost of 10 yearbooks $250 what is the cost of one yearbook
Answers
The cost is x and the amount is 10
So the equation is 10x=$250
Divide 250 by 10 and get 25
$250/10 = $25
_____
Whether you can actually purchase one yearbook for that price depends on a number of factors.
Joel is mailing a large envelope to his cousin. The envelope has pictures inside, so he doesn't want to bend it.
The mail slot has the dimensions shown. The dotted line shows the widest part of the slot.
Answers
Answer: 25
Step-by-step explanation:
Pythagorean theorem
c=√a²±b²
So it was 7=A
And it was 24=b
solving that it gives us 25
This isn’t that much of help sorry but this is the basic info on how to solve it you can learn more by searching videos about the Pythagorean thermom.
Hope this helps-A
The maximum width of the slot is 25cm (Option A).
To find the maximum width of the mail slot, we need to calculate the length of the diagonal (the dotted line) in the rectangle. The diagonal of a rectangle can be found using the Pythagorean theorem.
Given:
- The length of the rectangle (one side) = 24 cm
- The height of the rectangle (other side) = 7 cm
The formula for the diagonal [tex]\( d \)[/tex] is:
[tex]\[ d = \sqrt{(length)^2 + (height)^2} \][/tex]
Substituting the given values:
[tex]\[ d = \sqrt{24^2 + 7^2} \][/tex]
[tex]\[ d = \sqrt{576 + 49} \][/tex]
[tex]\[ d = \sqrt{625} \][/tex]
[tex]\[ d = 25 \, \text{cm} \][/tex]
So, the maximum width of the mail slot is 25cm.
Full Question:
Joel is mailing a large envelope to his cousin. The envelope has pictures inside, so he doesn't want to bend it.
The mail slot has the dimensions shown. The dotted line shows the widest part of the slot.
What is the maximum width of the mail slot?
A) 25
B) 31
C) 22
D) 20
a student has test scores of 92%, 87%, and 78%. what must she need to score on thenlast test to maintain 80% or better?
Answers
What’s 3.192 rounded to the nearest hundredth ?
Answers
Rex painting the garage in the shed he uses 3 gallons of paint on the garage he uses 3/4 of that amount on the shed enter the amount of paint in gallons Rex uses on the shed
Answers
0.75×(3 gallons) = 2.25 gallons
Rex uses 2.25 gallons of paint on the shed.
Rex uses 2.25 gallons of paint on the shed, which is [tex]\( \frac{3}{4} \)[/tex] of the 3 gallons of paint he uses on the garage.
To find out how much paint Rex uses on the shed, we need to calculate [tex]\( \frac{3}{4} \)[/tex] of the amount of paint he uses on the garage.
Rex uses 3 gallons of paint on the garage.
Therefore, the amount of paint he uses on the shed is:
Paint used on the shed = [tex]\frac{3}{4} \times 3[/tex]
Calculating this:
Paint used on the shed = [tex]\frac{3 \times 3}{4}[/tex]
= [tex]\frac{9}{4}[/tex]
= 2.25
So, Rex uses 2.25 gallons of paint on the shed.
PLEASE ANSWER!!! WILL MARK BRAINLIEST :D
When Alina was hungry she ate c cookies, which was 30% of all the cookies she had. How many cookies did she have in the beginning?
Answers
0.30a=x
x/0.30
This graph shows the solution to the inequalities y>3/2x-2 and y<3/2x-10. Does the system of inequalities have solutions? If so, which region contains the solution?
A) there is no solution
B) there is a solution, and it’s shown by region A.
C) there is a solution, and it’s shown by region C
D) there is a solution, and it’s shown by region B.
Answers
the region A satisfies only the inequality-------> y>3/2x-2
the region C satisfies only the inequality-------> y<3/2x-10
the region B
does not satisfy any of the two inequalities
there is no region that satisfies both inequalities
therefore
the answer is the option
A) there is no solution
Answer:
there is no solution
Step-by-step explanation:
A cylindrical thermos has a radius of2 in. and is 5 in. high. It holds 10 f oz. To the nearest ounce, how many ounces will a similar thermos with a radius of 3 in. hold? Show your work
Answers
A--------> larger thermos with radius 3 in
B-------> smaller thermos with radius 2 in
we know that
scale factor=radius larger thermos/radius smaller thermos
scale factor=3/2----> 1.5
volume larger thermos=[scale factor]³*volume smaller thermos
volume larger thermos=[1.5]³*10 f oz-----> 3.375*10-----> 33.75 f oz----> 34 f oz
the answer is
34 f oz
you have $120 to donate equally to several charities. Does this situaton represent direct or inverse variation? Explain.
Answers
The difference between direct and inverse variation is in direct variation, as one variable goes up the other does too, while in inverse, as one variable goes up the other falls.
In this case, as you donate to more charities, the amount you donate to each charity falls, because you donate an equal amount. This means it's inverse variation.
Hope this helps!
hey can you please help me posted picture of question
Answers
( 6 - 2i) + ( 11 + 6i)
= 6 + 11 - 2i + 6i
= 17 + 4i
So the answer to this question is option D
hey can you please help me posted picture of question
Answers
The steps to find the inverse are listed below.
[tex]f(x)= \frac{2x}{7}+4 \\ \\ y= \frac{2x}{7}+4 \\ \\ y-4= \frac{2x}{7} \\ \\ 7(y-4)=2x \\ \\ x= \frac{7(y-4)}{2} \\ \\ f^{-1}(y)= \frac{7(y-4)}{2} \\ \\ f^{-1}(x)= \frac{7(x-4)}{2} \\ \\ [/tex]
some help help help help help help help help help help help help help help help help help help help help me please please please some
Answers
Form a sequence that has two arithmetic means between -1 and 59.
a.
-1, 29, 29, 59
c.
19, -1, 59, 39
b.
-1, 19, 39, 59
d.
-1, 14, 29, 44, 59
Answers
an = a1 + (n - 1)d
Where:
n = number of figure in the sequence = 4
d = difference between successive number =?
a1 = -1
a4 = 59
Insert the given values into the formula,
59 = -1 + (4 - 1)d
59 = -1 + 3d
59 + 1 = 3d
60 = 3d
d = 60/3 = 20
Therefore, d = 20. This implies that, there is a difference of 20 between successive numbers.
The number sequence is as follow:
-1, 19, 39, 59.
b.-1, 19, 39, 59
a plumber has a 36in. pipe that he has to cut into two pieces so that one piece is 8 in. longer than the other. find the length of each piece?
Answers
and the other one is 14
What is the perimeter of the rectangle? Write your answer in scientific notation. The area is 2.76 x 10 pw12 the width is 4.6 x 10 pw5 pw is the power
Answers
You have
area = 2.76·10^12
width = 4.6·10^5
You want to find the perimeter of the rectangle with these dimensions.
The perimeter of a rectangle is twice the sum of length and width.
perimeter = 2*(length + width)
The length can be figured from the area using the formula for area.
area = length*width
area/width = length . . . . . . . . . divide by width
Filling in the numbers, we have
perimeter = 2*((2.76·10^12)/(4.6·10^5) +(4.6·10^5))
perimeter = 2*(6.0·10^6 +0.46·10^6)
perimeter = 2*6.46·10^6 = 1.292·10^7
The perimeter of the rectangle is ...
1.292·10^7
To calculate the perimeter of a rectangle in scientific notation, divide the given area by the width to find the length, then use the perimeter formula (P = 2×length + 2×width), accounting for the power of 10 in your calculations to maintain proper notation.
Explanation:The perimeter of a rectangle can be found using the formula P = 2×length + 2×width. Given the area of the rectangle (2.76 x 10^12 square units) and the width (4.6 x 10^5 units), we can find the length by dividing the area by the width. The length would therefore be the area divided by the width which is (2.76 x 10^12) / (4.6 x 10^5) = 6 x 10^6 units. Now that we have the length and width, we can calculate the perimeter by substituting into the formula: P = 2×(6 x 10^6) + 2×(4.6 x 10^5) = 1.2 x 10^7 + 9.2 x 10^5. Converting the width to the same power of 10, we get P = 1.2 x 10^7 + 0.092 x 10^7 = 1.292 x 10^7 units. This expresses the perimeter in scientific notation.
If Dr. Suzuki rides his bike to his office, he averages 9 miles per hour. If he drives his car, he averages 27 miles per hour. His time driving is one third hour less than his time bicycling. How far is his office?
Answers
Riding speed = 9 mph
Driving speed = 27 mph
Time
If x hours is the time taken when riding, (x - 1/3) hours is the time taken when driving.
Distance in both instances is the same, D= Speed * time
Therefore,
9*x = 27(x-1/3)
9x = 27x - 27/2
9x = 27x - 9
(9-27)x = -9
-18x = -9
x = 9/18 = 1/2 hours
Distance, D = 1/2 *9 = 4.5 miles
What are the dimensions of the image at fraction 1 over 2 times its current size?
Length = 4 inches, width = 5 inches
Length = 6 inches, width = 8 inches
Length = 10 inches, width = 12 inches
Length = 16 inches, width = 20 inches
Answers
Answer:
Length = 4 inches, width = 5 inches
Step-by-step explanation:
which is the coefficient in the algebraic expression 12x + z^4 ?
Answers
Hope this helps!
hey can you please help me posted picture of question
Answers
The correct answer for this completion exercise shown above is the second option (Option B), which is: B. Parent
Therefore, you have:"In each family of function, the parent function is the most basic function in the family"
By definition, the most basic fucntion in each family of functions is called “parent fucntion”. A family of function is a set of function that when you graph them, you can notice that they have common charateristics.
Michelle collects US, Canadian and Mexican stamps. In her collection 80% of the stamps are U.S. and Mexican stamps. there are 3 times as many U.S. stamps as Mexican stamps. WHat percent of Michelle's collections is made up of U.S. stamps?
Answers
The US stamps are 3 times the Mexican stamps. That means that of the 80%, Mexicans comprised of the 20% and US comprised of the 60% to satisfy the relationship of their ratios.
Therefore, 60% of Michelle's collection is made up of US stamps.
Final answer:
Michelle's stamp collection consists of 60% U.S. stamps, determined by solving equations based on the given information that U.S. and Mexican stamps make up 80% of her collection and there are three times as many U.S. stamps as Mexican stamps.
Explanation:
The student asked what percent of Michelle's stamp collection is made up of U.S. stamps if 80% are U.S. and Mexican stamps and there are 3 times as many U.S. stamps as Mexican stamps. To solve this, let's call the percentage of U.S. stamps 'U' and the percentage of Mexican stamps 'M'. According to the given information, U + M = 80%, and U = 3M.
We substitute the second expression into the first to get 3M + M = 80%, which simplifies to 4M = 80%. Dividing both sides by 4 gives M = 20%. As the number of U.S. stamps is three times the number of Mexican stamps, we calculate U as 3 × 20% = 60%. So, the percentage of U.S. stamps in Michelle's collection is 60%.
Marisol and Mimi walked the same distance from their school to a shopping mall. Marisol walked 2 miles per hour, while Mimi left an hour later and walked 3 miles per hour. If they reached the mall at the same time how far is the mall from their school?
Answers
The distance walked by Marisol=speed*time=2t
Distance walked by Mimi=3(t-1)
When they've reached school they've all walked the same distance so:
3(t-1)=2t
3t-3=2t
3t-2t=3
t=3
Thus the distance from the mall to their school is 2t=2*3=6 miles
Which ordered pair is a solution of y = x - 4?
( -3, -7 )
( 3, -7 )
( -3, 7 )
( 3, 7 )
Answers
an order pair follows the (x, y) pair, in which (in this case), x = -3, and y = -7
plug in to the respective places inside the equation.
y = x - 4
(-7) = (-3) - 4
-7 = -7 (true)
Therefore, (-3, -7) is your answer
hope this helps
[tex]42 \times 42 \times 29 = [/tex]
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Hope this helps :)