Answers
9514 1404 393
Answer:
a) f: all real numbers except 1 and 2; g: all real numbers except 2
b) f(x) = 5/(x -2) . . . . x = 2 is a vertical asymptote
c) f(x) = -5/4, -5/3, -5/2, undefined, undefined, 5, 5/2
g(x) = -5/4, -5/3, -5/2, -5, undefined, 5, 5/2
d) f(x) is also undefined at x=1
Step-by-step explanation:
a) Any question about the domain of a function concerns the values of the variable for which the function is defined, or not. A rational function, such as these, will be undefined when its denominator is zero. So the question of domain becomes a question of the values of x that make the denominator zero.
The zeros of the denominator of f(x) can be found by factoring it.
x^2 -3x +2 = (x -1)(x -2)
These factors are zero when x=1 and when x=2. Hence, these values are excluded from the domain of f(x).
domain of f(x): all real numbers except x=1 and x=2
Then, by inspection, the domain of g is similar, but a little different:
domain of g(x): all real numbers except x=2
__
b) Based on our work for part (a), we find that f(x) can be factored and simplified like this.
[tex]f(x)=\dfrac{5x-5}{x^2-3x+2}=\dfrac{5(x-1)}{(x-1)(x-2)}\\\\\boxed{f(x)=\dfrac{5}{x-2}\quad x\ne1}[/tex]
There will be a vertical asymptote at x=2. The attachment shows a graph of f(x) with its vertical asymptote.*
__
c) The difference between the two functions is that f(x) is undefined at x=1.
x = -2, -1, 0, 1, 2, 3, 4
f(x) = -5/4, -5/3, -5/2, undef, undef, 5, 5/2
g(x) = -5/4, -5/3, -5/2, -5, undef, 5, 5/2
__
d) The functions differ in that f(x) is undefined at x=1, whereas g(x) is not.
_____
* The fact that f(x) is undefined at x=1, but there is no vertical asymptote at that point, means the function has a "hole" in its graph there. This is illustrated on the graph by an open circle, meaning the function is not defined at that point.
Related Questions
HELP PLEASE PICTURE EXPLAINS EVERYTHING!!!!
Answers
Answer:
(a) Slope of Line 1 = 3
Slope of Line 2 = 3
Slope of Line 3 = -1/3
(b)
Line 1 and Line 2 = Parallel
Line 1 and Line 3 = Perpendicular
Line 2 and Line 3 = Perpendicular
Step-by-step explanation:
Please mark as brainliest! Thanks! Hope this helps!
Substitute to solve
Brainliest for correct answer
Answers
Answer:
4x-1y=3xy
Step-by-step explanation:
because 3-2=1 and add the y on and the do 4x-1y and that will = 3xy
Answer:
x=4, y=6
Step-by-step explanation:
hope that helps :)
Can someone please explain how to find the answer? My old teacher didn’t do it this way and I’m lost :/
Answers
Answer:
the triangle means "change in". so triangle x means the change in the x values and triangle y means change in y values so yeah mental calculate the difference
Find the density of a book with a mass of 24g and a volume of 5cm'.
Solve:
Given:
(24g) (5cm^3)
Answers
Answer:
The answer is 4.8 g/cm³Step-by-step explanation:
The density of a substance can be found by using the formula
[tex]density = \frac{mass}{volume} \\ [/tex]
From the question we have
[tex]density = \frac{24}{5} \\ [/tex]
We have the final answer as
4.8 g/cm³Hope this helps you
Answer: 1.2 × 10-7 m3 kg
Step-by-step explanation:
(24g) (5cm^3)=1.2 × 10-7 m3 kg
Help Help!!!
will Give uh brainliest
Answers
Answer:
First one: A 4 in 12 chance
Step-by-step explanation:
Answer:
1/3
Step-by-step explanation:
The coin was flipped 12 times. Out of the 12, Tashi tagye was gotten 4 times. That will be 4/12. Reducing to the lowest tem will get 1/3
A dressmaker needs to cut 6-inch pieces of ribbon from rolls of ribbon that are 9 feet in length. How many 6-inch pieces can the dressmaker cut from 15 of these rolls of ribbon? Before you try that problem, answer the question below. How many inches of ribbon does the dressmaker have, in total?
Answers
Answer:
Step-by-step explanation:
Answer:
60 pieces
Step-by-step explanation:
What we know:
There are 12 inches in a foot
There are 5 6-feet lengths of ribbon
So, we simply need to multiply.
Since there are 12 inches in a foot, and we only need 6 inches for each one, we can see that she makes 2 pieces for each foot.
Multiply
2*6=12
She makes 12 pieces for each length of ribbon.
Now multiply it by 5
12*5= 60
She can make 60 pieces from 5 of these length of ribbon.
Hope this helps!
50 POINTS PLEASE HELP
Stephano solved this inequality, but the solution does not work when he checked his answer. In which step did he go wrong? Explain.
-4s + 5 ≤ 16
\frac{-4s + 5}{-4} ≥ \frac{16}{-4}
s + 5 - 5 ≥ -4 - 5
s ≥ -9
Answers
Answer: 2nd step
Step-by-step explanation:
(-4s+5 )/-4 ≥ 16/-4
S-(5/4) ≥ -4
S ≥ -4+(5/4)
S ≥ 1/4
can someone help thank you!
Answers
Answer:
Step-by-step explan
HELP PRETTY PLEASSSEEE
Answers
Answer: b.) 14
Step-by-step explanation:
Answer:
14
Step-by-step explanation:
The absolute value is always positive and 18-4 =14
What is the value of x?
Enter your answer in the box.
Answers
Answer:
111°
Step-by-step explanation:
The polygon given is a heptagon having 7 sides.
Sum of interior angles of a 7-sided polygon = (n - 2)*180
= (7 - 2)*180
= 5*180 = 900°
Therefore:
126° + 158° + 120° + 125° + 121° + 139° + x° = 900°
Solve for x
789° + x° = 900°
Subtract 789 from each side
x = 900° - 789°
x = 111°
Find the equation of the linear function represented by the table below in slope-intercept form. x y -1 3 1 1 3 -1 5 -3
Answers
Answer:
y = - x + 2Step-by-step explanation:
Points given:
(-1, 3), (1, 1), (3, -1), (5, -3)Slope-intercept form:
y = mx + bFinding the slope using slope formula and the first two points:
m = (1 - 3)/(1 - (-1)) = -2 / 2 = -1Finding y-intercept using the slope and the first point:
3 = (-1)*(-1) + b3 = 1 + bb = 3 - 1b = 2So the equation is:
y = - x + 2arrange the following from least to greatest (integers)
44,16,-8 and -20,8,0,-3
Answers
Answer:
-20, -8, -3, 0, 16, 44
Step-by-step explanation:
Write the equation that represents a 15% increase of $120.
Answers
Answer:
$138
Step-by-step explanation:
if 100 is 15 then you add 1.15 or 1% of 15
PLEASE HELP ILL GIVE BRAINLIEST
Answers
Answer:
1. x = 66
2. C
3. C. 2000
Step-by-step explanation:
1. The first question is x = 66 because to get rid on the fraction you multiply both sides by 4. This leaves you with x + 2 = 68 (minus 2 on both sides) this gives you x = 66.
2. C. Commutative
3. 2000
Plug in
125 = (5)(.0125)(2000)
125 = 125
Hope this helps ya!!
100 % if my grade and giving brainliest if answered correctly please helppp im failing
Answers
Answer:
Hope I'm not too late for this...
(look below)
Step-by-step explanation:
For the first part:
1. b = -1, m = 2
The y-intercept (b) is the value of y when x = 0. In this case, we can see that when x = 0, y = -1 so the y-intercept is -1.
The slope was found using the equation slope (m) = (y2-y1) / (x2-x1) and two points. (Note, you can choose any two points, I just chose the first two.)
(5,9) (-2,-5)
slope = (y2-y1) / (x2-x1)
slope = (-5-9) / (-2-5)
slope = -14/-7
slope = 2
I used the same steps as shown above:
2. b = 2, m = -3
For the second part:
1. y = 2x - 1
2.y = -3x + 2
I basically plugged in the values for m and b into the equation, y = mx + b.
Graphs:
The way to graph a line is to plot at least two points and draw a line through them. You can graph it using either the equation or the table. I used the table since it is much easier to find the points that I need.
Below I have included references to what the graph should look like if you need to check your work.
The one in blue is for the equation y = 2x - 1. This should help you get a visual of what the correct graph looks like.
The one in green is for the equation y = -3x + 2.
I hope this helped!
(9x2 – 8) + (9x2 + 9x + 3)
Answers
Answer:
18x2 +9x -5
Step-by-step explanation:
combine like terms
Find the slope and y-intercept of the line in each graph.
PLEASE HELP ASAP
Answers
Answer:
slope m = -2, y-intercept b = 1
Step-by-step explanation:
The slope is the change in y over the change in x.
Equation for slope: y2-y1/x2-x1=m
Since they already gave us the two points we just have to decide which one is our y2,y1 and out x2,x1 (which one you chose does not matter). And plug the numbers into the equation and get: -3-1/2-0=m, in this case, m=-4/2 and simplify it into -2. Now we have our slope.
The y-intercept is where the line crosses over the y-axis, and in our case, it is given to us in the (0,1) so our slope is 1.
Hope this helps you
what number do these base ten blocks show
Answers
For the month of June, a music supply company is promoting the launch of its electronic music club by offering new members two options for downloading music.
Option #1: Annual club membership at a fee of $125 per year plus an option of prepaying for unlimited music downloads at a rate of $10 per month.
Option #2: Annual club membership at a fee of $50 per year plus an option of prepaying for music downloads at a rate of $1 per song.
You decide to join the electronic music club for one year, but aren’t sure which membership option is best suited for your music downloading needs. Review both options that the music supply company is offering for its new club members. Use the information provided to respond to the following prompts. When necessary, answer in complete sentences and include all calculations.
Write a function that best models the total cost of club membership plus downloads under option #1.
For membership option #1, calculate the total cost for one year of club membership and prepaid unlimited music downloads.
Write a function that best models the total cost of club membership plus downloads under option #2
Calculate the maximum number of music downloads that you will have with one year of club membership under option #2 for the same annual cost of a membership with unlimited downloads.
Over the past year, you downloaded an average of 14 songs per month. Assuming that for the next year, you continue to download music at the same rate per month, which membership option is most cost effective?
Answers
Answer:
six points for all this ? HAHAHAHAHA LFMAO
Step-by-step explanation:
I WILL GIVE BRAINLIEST. I NEED ANSWER ASAP.
Answers
I believe it is C :)
two shapes that represent the cross-sections
Answers
Answer:
it's the square and the rectangle
use the function below to find f(-2).
f(x)=3^x
Answers
hi
f(x) = 3^(x) so (f-2) = 3^(-2) = 1/ 3² = 1/9
Answer: 1/9
Step-by-step explanation:
Sara halves it and gets an answer of 34.3. What was the original number?
please help me im doing hegarty maths and I dont know what is this answer please help me
Answers
because 34.3 times 2 is that or if u divide 68.6 by 2 u get 34.3
Patty is inviting her friends to a party. She has 30 snack bars 45 juice boxed, and she wants to give the same number of each item to each friend.
Answers
Example: 10 friends
30/10= 3 so 3 snack bars
45/10=4.5 so 4 juice boxes
From a room temperature of 42 degrees, the temperature dropped by 20 degrees, then rose by 75 degrees and finally dropped by 1 degree. What is the temperature after the given changes?
Answers
I need help on this question can you tell me what the blanks are pls
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Answer:
sorry I wish I can help you
Step-by-step explanation:
ANSWER ASAP !! NEED HELP ASAP
Answers
Answer:
130
Step-by-step explanation:
The two angles add up to be 180 degrees, so you could find the value of the second angle to be 110 degrees, but it is asking for the x value so you would choose 130 since when you subtract 20 from 130 you get 110.
The ratio of women to men at a college is 9 to 8. If there are 5,644 students in the school, how many more women are there than men?
Answers
Answer:
78
Step-by-step explanation:
5,644 divided by 9 = 627
5,644 divided by 8 = 705
705 - 627 = 78
Hope this helps
mark brainliest please
Guys pls help me im failing my grade and i really need help plsssss and dont do it for the points
Answers
Answer:
simplified: [tex]\frac{3}{5}[/tex]
unsimplified: [tex]\frac{12}{20}[/tex]
Step-by-step explanation:
Since the fractions have the same denominator, all we have to do is subtract the numbers in the numerator:
15 - 3 = 12
The difference of the two fractions is [tex]\frac{12}{20}[/tex]. To simplify this answer, divide both the numerator and the denominator by 4:
12/4 = 3
20/4 = 5
The difference in simplified form is [tex]\frac{3}{5}[/tex].
I hope this helps. :)
What is the slope-intercept equation of the line (easy?)
Brainliest if right
Answers
Answer:
y = 1x + 2
Step-by-step explanation:
did i get it right?
Answer:
[tex]y=\frac{3}{4} x+2[/tex]
Step-by-step explanation:
y=mx+b
We have two points (0,2) and (4,5).
2=m(0)+b --> So b=2
5=4m+2
4m=3
m=[tex]\frac{3}{4}[/tex]
[tex]y=\frac{3}{4} x+2[/tex]