Find the domain and range of f(x). Please explain your answer.
f(x) = √(x^2+5x+6)
Answers
Answer:
Domain:— [ x ≥ -2, x ≤ -3 ]
Range:— [ y ≥ 0 ]
Step-by-step explanation:
You may use graphing calculator to draw a graph and examine the graph’s domain and range. However, I’ll explain further about the graph of quadratic in a surd.
First, factor the quadratic expression in the surd:—
[tex]\displaystyle \large{f(x)=\sqrt{(x+3)(x+2)}}[/tex]
We can find the x-intercepts by letting f(x) = 0.
I’ll be separating in two parts — one for finding x-intercept and one for finding y-intercept.
__________________________________________________________
Finding x-intercepts
Let f(x) = 0.
[tex]\displaystyle \large{0=\sqrt{(x+3)(x+2)}}[/tex]
Solve for x, square both sides:—
[tex]\displaystyle \large{0^2 = (\sqrt{(x+3)(x+2)})^2}\\\displaystyle \large{0=(x+3)(x+2)}[/tex]
Simply solve a quadratic equation:—
[tex]\displaystyle \large{x=-3,-2}[/tex]
Therefore, x-intercepts are:—
[tex]\displaystyle \large{\boxed{x=-3,-2}}[/tex]
__________________________________________________________
Finding y-intercept
Let x = 0.
[tex]\displaystyle \large{f(x)=\sqrt{(0+3)(0+2)}}\\\displaystyle \large{f(x)=\sqrt{3 \cdot 2}}\\\displaystyle \large{f(x)=\sqrt{6}}[/tex]
Therefore, y-intercept is:—
[tex]\displaystyle \large{\boxed{\sqrt{6}}}[/tex]
__________________________________________________________
However, I want you to focus on x-intercepts instead. We know that the square root only gives you a positive value. That means the range of function can only be y ≥ 0.
For domain, first, we have to know how or what the graph looks like. You can input the function in a graphing calculator as you’ll see that when x ≥ -2, the graph heads to the right while/when x ≤ -3, the graph heads to the left. This means that the lesser value of x-intercept gets left and more value get right.
See, between -3 < x < -2, there is no curve, point or anything between the interval. Therefore, -3 < x < -2 does not exist in function.
Hence, the domain is:—
x ≥ -2, x ≤ -3
Related Questions
Can someone please help me with this???
1.
Part A: If (26)x = 1, what is the value of x? Explain your answer. (5 points)
Part B: If (50)x = 1, what are the possible values of x? Explain your answer. (5 points)
Answers
Part A:
(26)x = 1
Solve for x by dividing both sides by 26:
X = 1/26
part B:
(50)x = 1
Solve for x by dividing both sides by 50:
X = 1/50
[tex]\\ \rm\Rrightarrow 26x=1[/tex]
[tex]\\ \rm\Rrightarrow x=1/26[/tex]
#B
[tex]\\ \rm\Rrightarrow 50x=1[/tex]
[tex]\\ \rm\Rrightarrow x=1/50=0.02[/tex]
Is the equation y/x=8 direct variation, inverse variation, or neither? Explain
Answers
Answer:
It's a direct variation, as the ratio between x and y is constant
Penelope is now 3 times the age of jaslin. If jaslin will be 12 in 3 years, how many years ago was Penelope 13 years ago?
Answers
Answer:
Penelope is 14 years old.
Step-by-step explanation:
- Jaslin is 9 years old (since she'll be 12 in 3 years)
- So, you multiply 9 by 3 (since Penelope is 3 times Jaslin's age), which gives you 27.
- Then minus 13 from 27 (since we're solving for how old Penelope was 13 years ago), which gives you 14
Hope this helps!
Find sine and cosine if angle C please
Answers
Answer: sin=7/13,cos=2.sqrt30/13
Step-by-step explanation:
SOH COH TOA
sin=opp/hyp,cos=adj/hyp
Use pyth. theorem to find the adjacent of C.
13^2 =7^ + b^2
169 = 49 + b^2
120 = b^2
sqrt120 = sqrtb
2.sqrt30 = b is the missing side.
30 POINTS!!
Create one equation with the distributive property and show the work to solve it.
Answers
Answer:
173
Step-by-step explanation:
6+4/8*2+(4+9)^2-3
6+4/8*2+13^2-3
6+4/8*2+169-3
6+1/2*2+169-3
6+1+169-3
173
3(x + 5)
The distributive property states that you are distributing whatever is outside the parenthesis to all terms within the parenthesis. For complex distributive questions, you will have to simplify the parenthesis first (if you can) before distributing.
In this case, the example given is 3(x + 5).
First, distribute 3 to all terms in the parenthesis by multiplication:
3(x + 5)
= (3 * x) + (3 * 5)
= 3x + 15
3x + 15 is your answer.
~
Another more complex distribute property can involve powers. Take for example:
(7x + 5)²
In this case, you will use the distributive method of FOIL, or (First, Outside, Inside, Last). Set the question:
(7x + 5)² = (7x + 5)(7x + 5)
First: 7x * 7x = 49x²
Outside: 7x * 5 = 35x
Inside: 5 * 7x = 35x
Last: 5 * 5 = 25
Next, combine like terms:
49x² + 35x + 35x + 25
49x² + (35x + 35x) + 25
49x² + (70x) + 25
49x² + 70x + 25 would be your answer.
~
find the value of x
Answers
Answer: 3
Step-by-step explanation:
Can someone help me with this?
Answers
HELPPP FOR BRIANLEST!!!!
Answers
Answer:
4/13
Step-by-step explanation:
NOT 2010s and NOT spruce wood (4) over total (13)
4/13 is in its reduced form
The largest Ferry in the puget Sound fleet can carry 2,500 passengers every hour
Answers
Answer:
A: 2,500×H. B=20,000 passengers
A colony of microbes doubles in population every 6 hours. Explain why we could say that the population grows by a factor of 6 square 2 every hour.
Answers
Answer:
please mark brainlyest
6 = 200
12 = 400
18 = 800
24 = 1600
30 = 3200
36 = 6400
42 = 12800
48 = 25600
In theory assuming none of them die and they reproduce at a constant rate.
In the given rate of 12,060 cows per 30 farms, what would be the unit rate per farm?
Answers
Answer:
402 cows per farm
Step-by-step explanation:
12060/30
=402
Find the surface area of a rectangular prism with a length of 13 ft,
width of 8 ft and height of 18 ft.
Answers
Length:13 ft
Width:8 ft
Height:18 ft
Find the perimeter of a rectangle whose length and breadth are 9.6 cm and 7.9 cm respectively.
Answers
Question :-
Find the Perimeter of a Ractangle whose Length and Breadth are 9.6 cm and 7.9 cm respectively .Answer :-
Perimeter of a Ractangle is 35 cm .[tex] \rule {210pt} {2pt} [/tex]
Given :-
Length of Rectangle = 9.6 cmBreadth of Rectangle = 7.9 cmTo Find :-
Perimeter of Rectangle = ?Solution :-
As per the provided information in the given question, we have been given that Length of Rectangle is 9.6 cm . Breadth of Rectangle is given 7.9 cm . And, we have been asked to calculate the Perimeter of Rectangle .
For calculating the Perimeter , we will use the Formula :-
[tex] \bigstar \: \: \boxed {\sf { \: Perimeter \: _{Rectangle} = 2 \times [ \: Length + Breadth \: ] \: }} [/tex]
Therefore , by Substituting the given values in the above Formula :-
⇒ Perimeter = 2 × [ Lenght + Breadth ]
⇒ Perimeter = 2 × [ 9.6 + 7.9 ]
⇒ Perimeter = 2 × 17.5
⇒ Perimeter = 35
Hence :-
Perimeter = 35 cm .[tex] \underline {\rule {210pt} {4pt}} [/tex]
Note :-
Kindly scroll the Screen form Right to Left direction for Better View .Tyler solved an inequality to determine the number of songs he can buy with a $20 credit at his favorite music website. The solution is graphed below. A number line going from 5 to 13. A solid circle is at 8. Everything to the left of the circle is shaded. Which phrases accurately describe all the possible quantities of songs he can buy? Select two options. No more than 8 songs at least 8 songs a minimum of 8 songs at most 8 songs fewer than 8 songs.
Answers
Tyler can buy at most 8 songs.
We have given that,Tyler solved an inequality to determine the number of songs he can buy with a $20 credit at his favorite music website.
What is the meaning of inequality?inequality, In mathematics, a statement of an order relationship greater than, greater than or equal to, less than, or less than or equal to between two numbers or algebraic expressions.
A number line going from 5 to 13.
A solid circle is at 8.
Therefore,from the given we can say that,
he cannot buy no more than 8 songs.
Therefore,Tyler can buy at most 8 songs.
To learn more about the inequality visit:
https://brainly.com/question/20519560
Work out
(4 x 10-1) + (4 x 10-1)
Give your answer in standard form.
Answers
= 8 x 10-1
Q2 ) A cylinder with a diameter of 4 ft , and height of 6 ft . Find the VOLUME and SURFACE are of the cylinder .
Answers
Answer:
The volume is ten(10)and the surface is also ten(10)
Jack burned 150 calories on the elliptical and 210 calories on the treadmill. What do a the ratio of calories burned on the elliptical to calories burned on the treadmill?
Answers
Answer:
5/7
Step-by-step explanation:
When you reduce 150/210 you get 5/7, this is the reduced form
find the volume of the cone
Answers
The volume of the cone is [tex]\frac{1}{3} \pi r^{2}h[/tex]
r: radius --> 6fth: height --> 6ft[tex]\pi[/tex] = 3.14Volume = [tex]\frac{1}{3} \pi (6)^{2} *6=226.08ft^{3}[/tex]
Hope that helps!
9 + 4 to the third power x (20-8) / 2 + 6
Answers
Answer:
120.25
Step-by-step explanation:
4 to the third power is 64. so 64 + 9 = 83. 20-8 = 18. 6 + 2 = 8.
so 83 + 18 + 8 = 109. so 8 divided by 18 = 2.25. 109 + 9 + 2.25 = 120.25.
HELP ME FIND THE AREA I AM DESPERATE QUESTION IN LINK
Answers
Answer:
4π cm²
Step-by-step explanation:
The area of a circle is [tex]\pi r^2[/tex], where r = radius. We're given the radius as 2 centimeters, and we have to solve in terms of pi.
[tex]2^2 * \pi[/tex] [tex]4*\pi[/tex] [tex]4\pi[/tex] 4π cm²Therefore, the answer is 4π cm².
PLEASE HELP Giving 50 POINTS PLEASE EXPALIN ANSWER
Answers
PART 1: Julie is incorrect ; 15/4 ≠ 3/2
PART 2: LIZ IS CORRECT
What values are needed to make each expression a perfect square trinomial? x2 4x x2 – 10x.
Answers
Answer:
Step-by-step explanation:
4 and 25
In a math test, there are 16 multiple-choice problems. Correct answer will get 6 points, and wrong answer will deduct 2 points, and leaving the question not answered will get 0 point. Stan has one question not answered, at least how many correct answer(s) should he get in order to get total score not less than 60
Answers
So if he has one question not answered that stays at 0 points+ however many points he already has. He has to get at least 10 questions right. 10x6= 60
Manny's Restaurant bought 9 1/4 pounds of onions. The restaurant bought 7 3/4 times as much potatoes as onions. How many pounds of potatoes did the restaurant buy?
Answers
Answer:
71.6875 pounds of patatoes.
Step-by-step explanation:
9.25x7.75 = 71.6875
A cube with 2 meters.explain what happens to the volume of the cube if the length of the sides is doubled pls answer this for me
Answers
Answer:
The volume will be multiplied by 8.
Step-by-step explanation:
If the sides are doubled, what is going to happen to the volume? First, let's find out what the initial volume is first!
The side lengths are 2 meters. With squares/cubes, all sides are equal.
So, the length, height, and width are the same.
For the volume, we need to multiply those values.
2*2*2=8 meters
That's the initial volume.
Now, let's find out what the volume will be once we've double the side values.
2*2=4
The side values are now four.
Let's multiply!
4*4*4=64 meters
It looks like the volume multipled by eight fold.
What is the approximate length of arc s on the circle? 5. 23 in. 41. 87 in. 52. 36 in. 104. 67 in.
Answers
Answer:
need PPO
Step-by-step explanation:
need points I am 5 grade student sorry
0.32 with the 2 repeating as a fraction
Answers
Answer:
29/90
Step-by-step explanation:
Use the formula:
((DN x F) - NRP)/D
DN = Decimal Number
F = 10 if one repeating number, 100 if two repeating numbers, 1000 if three repeating numbers, etc.
NRP = Non-repeating part of decimal number.
D = 9 if one repeating number, 99 if two repeating numbers, 999 if three repeating numbers, etc.
((0.32 x 10) - 0.3)/9
= 2.9/9 = 29/90
Determine the value of ∠EBD∠EBD. Show your work.
Giving 18 POINTS
Answers
The value of ∠EBD is 66°
Vertically opposite anglesVertical angles are a pair of opposite angles formed by intersecting lines. Vertical angles are equal. Therefore,
∠EBA≅∠CBF
Therefore,
∠EBA = 40 - x
∠EBA + ∠EBD = 90°(complementary angles)
Therefore,
40 - x + 6x - 30 = 90
5x = 90 + 30 - 40
5x = 80
x = 80 / 5
x = 16
Therefore,
∠EBD = 6(16) - 30 = 66°
learn more on angles here: https://brainly.com/question/10987237
A game you is on sale for 15% off if the regular price is $50.00, how much will u save and what will the total sale price be
Answers
Answer:
you will save 7.50$ and the sales price will be 42.50$
Step-by-step explanation:
15% of 50 is 7.5
What is the solution to this inequality? 3x+7>16 Drag and drop a symbol and number to correctly complete the inequality.
PLEASE HELP!
Answers
Answer:
x > 3
Step-by-step explanation:
Step 1: Subtract 7 from both sides.
[tex]3x+7-7 > 16-7[/tex] [tex]3x > 9[/tex]Step 2: Divide both sides by 3.
[tex]3x/3 > 9/3[/tex] [tex]x > 3[/tex]Therefore, the solution is x > 3.
Answer:
[tex]\displaystyle 3 < x[/tex]
Step-by-step explanation:
[tex]\displaystyle 3x + 7 > 16 \hookrightarrow \frac{3x}{3} > \frac{9}{3} \\ \\ x > 3[/tex]
The above answer is written in reverce, and is still the same result.
*Now, in case you did not know how we arrived at the division, seven was deducted from both sides of the inequality to give you [tex]\displaystyle 3x > 9.[/tex]From there, we splat both sides in third to give you the above result.
I am joyous to assist you at any time.