The required sets of range of the corresponding functions are illustrated in the below solution part.
What is the range of a function?The range of a function is the set of all possible output values of the function.
To find the range of a function, we need to evaluate the function at every point in its domain and find the set of all possible output values.
For example, we are given the function f(x) = x² - 2x and the domain (-5, -1, 0, 5, 7). To find the range of this function, we need to evaluate it at every point in its domain, which gives us the following values:
f(-5) = (-5)² - 2 × (-5) = 25 + 10 = 35
f(-1) = (-1)² - 2 × (-1) = 1 + 2 = 3
f(0) = (0)² - 2 × (0) = 0
f(5) = (5)² - 2 × (5) = 25 - 10 = 15
f(7) = (7)² - 2 × (7) = 49 - 14 = 35
The range of the function is therefore the set of all possible output values, which are 3, 0, 15, and 35. Therefore, the range of this function is {3, 0, 15, 35}.
We can use the same method to find the range of the other functions in the questions. The ranges of the other functions are:
6) f(x)=x²-2x & Domain= (-5, -1, 0, 5, 7)
Range: {-1, 3, 0, 15, 35}
7) f(x) = -3x+12) & Domain= (-9, -4, 4, 8, 11)
Range: {0, 15, 36, 39, 48}
8) f(x)=x²-(x/2) & Domain = {4, 8, 12, 30)
Range: {2, 30, 102, 942}
9) f(x)= |x-2x & Domain= (-5, -4,-3, 3, 5)
Range: {-4, -3, 0, 3, 4}
10) f(x) = (x²/2) + 30 & Domain = {-4, -2, 6, 8)
Range: {26, 28, 54, 60}
Thus, the required sets of range of the corresponding functions are illustrated in the above solution part.
Learn more about the domain and the range here:
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Calculate the mean for each set of data.
a 12, 18, 9, 14, 8, 7
Answer:
11.3, rounded
Step-by-step explanation:
mean = average. Add them all up, then divide by how many entries/data points you have.
12 + 18 + 9 + 14 + 8 + 7 = 68
There are 6 numbers we added, so 68/6 = 11.3333333
Please let me know if you have questions.
What is the image point of (9,5) after a translation right 4 units and up 4
units?
Answer:
5,9
Step-by-step explanation:
can someone pleease help my teacher will not help me.
Answer:
The perimeter is 206.
Step-by-step explanation:
When given the area, height and side of the parallelogram, you would use the formula to find the perimeter: P=2a+2*A /h. a = side of the parallelogram, A = area, and h = height. When you plug in everything, you will get 206.
0.4209" to the nearest common fraction
Answer:
4209/10000
Step-by-step explanation:
42.09%=4209/10000
PLEASE HELP ASAP HELPPPPP PLEASEEE!!!! find the value of x. round to the nearest tenth
x
12
4
x =?
Answer:
70.5
Step-by-step explanation:
cos x = [tex]\frac{4}{12}[/tex]
x = [tex]cos^{-1}\frac{1}{3}[/tex]
x = 70.53
help please!!
Integrate the following:
[tex] \displaystyle \int {x}^{2} {e}^{x} dx[/tex]
Answer:
[tex] \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} {e}^{x}- 2x {e}^{x} + 2 e^{x} + \rm C[/tex]
Step-by-step explanation:
we want to integrate the following integration:
[tex] \displaystyle \int {x}^{2} \cdot {e}^{x} dx[/tex]
notice that, the integrand is in the multiplication of two different function in that case we can consider integration by parts given by:
[tex] \rm \displaystyle \int u \cdot v \: dx = u \int vdx - \int u' \left( \int v dx \right)dx[/tex]
where u' can be defined by the differentiation of u
now we have to choose our u and v
which can be chosen by using the guideline:ILATE Inverse trig. , Logarithm, Algebraic expression, Trigonometry, Exponent.
since x comes first thus,
[tex] \displaystyle u = {x}^{2} \quad\text{and} \quad v = {e}^{x} [/tex]
by figuring out the defferentiation of u,we acquire:
[tex] \displaystyle u' = 2x[/tex]
altogether we get:
[tex] \rm \displaystyle \int {x}^{2} \cdot {e}^{x} \: dx = {x}^{2} \int {e}^{x} dx - \int 2x \left( \int {e}^{x} dx \right)dx[/tex]
by figuring out the parentheses integration
we get:
[tex] \rm \displaystyle \int x^2 \cdot {e}^{x} \: dx = {x}^{2} \int {e}^{x} dx - \int2x \cdot {e}^{x} dx[/tex]
now we again have integration of two different functions so let's choose our u and v once again which can be done using the guideline
[tex] \displaystyle u = 2x \quad\text{and} \quad v = {e}^{x} [/tex]
by figuring out the defferentiation of u
we acquire:
[tex] \displaystyle \: u' = 2[/tex]
altogether we get:
[tex] \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} \int {e}^{x} dx - \left( 2x \int{e}^{x} dx- \int2 \left( \int{e}^{x}dx \right) dx \right)[/tex]
by solving parentheses we get
[tex] \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} \int {e}^{x} dx - \left( 2x {e}^{x} - 2 e^{x} dx \right)[/tex]
by figuring out the integral we get:
[tex] \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} {e}^{x}- \left( 2x {e}^{x} - 2 e^{x} \right)[/tex]
remove parentheses:
[tex] \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} {e}^{x}- 2x {e}^{x} + 2 e^{x} [/tex]
at last we of course have to add constant of integration:
[tex] \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} {e}^{x}- 2x {e}^{x} + 2 e^{x} + \rm C[/tex]
and we are done!
Answer:
[tex]\displaystyle \int {x^2e^x} \, dx = e^x(x^2 - 2x + 2) + C[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integration
IntegralsIndefinite IntegralsIntegration Constant CIntegration by Parts: [tex]\displaystyle \int {u} \, dv = uv - \int {v} \, du[/tex]
[IBP] LIPET: Logs, inverses, Polynomials, Exponentials, TrigTabular IntegrationStep-by-step explanation:
*Note:
The answer below me is correct, but there is a simpler method of obtaining the answer.
Step 1: Define
Identify
[tex]\displaystyle \int {x^2e^x} \, dx[/tex]
Step 2: Integrate
Use tabular integration.
[Integrand] Differentiate/Integrate [Tabular Integration]: [tex]\displaystyle \\\begin{center}\begin{tabular}{ c | c }\line{u & dv} \\\cline{1 - 2} x^2 & e^x \\\ 2x & e^x \\\ 2 & e^x \\\ 0 & e^x\end{tabular}\end{center}[/tex]Write out expansion [Tabular Integration]: [tex]\displaystyle \int {x^2e^x} \, dx = x^2e^x - 2xe^x + 2e^x + C[/tex]Factor: [tex]\displaystyle \int {x^2e^x} \, dx = e^x(x^2 - 2x + 2) + C[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
A muffin recipe calls for 1 cup of flour, 1/2 cup of sugar and 3/4 cup of milk and makes 20 muffins. How much of each ingredient would you need to make 120 muffins?
Answer:
well you multiple 20 by 6 to get 120, so that means multiple everything by 6
SO, 6 cups of flour, 3 cups of sugar, and 4 1/2 cups of milk
what is m∠ BAC???????
Answer:
36 degrees
Step-by-step explanation:
I’m pretty sure that’s it
Find the value of x.
Answer:
The answer would be X= -7 .
Step-by-step explanation:
Hope it helps :)
Solve for all values of x by factoring.
x^2+10x+12=2x+5
Answer:
x = -1, -7
Step-by-step explanation:
=> x² + 8x + 7 = 0
=> (x + 1) (x + 7) = 0
=> x = -1, -7
Plzzz help me!!! ASAP
What is the answer. No links please.
Answer:
24 + 50 = 74 cm³
Step-by-step explanation:
I split the irregular figure into two separate shapes and found the volume of each and then added the values, I am most certain the answer would be 74 cm³, I apologize if it isn't.
I need help on this ASAP
75cm²
Explanation:
10 times 15 is 150 and since it is a triangle you divide in half so the answer is 75. And in this case the 18 is not needed.
Answer:
75cm²
Step-by-step explanation:
The area A of a triangle is given by the formula A=12bh where b is the base and h is the height of the triangle. But in this case, there are three sides.
To find the area of a triangle with 3 sides given as 10, 15, and 18, we assume that a = 10, b = 15, and c = 18.
Then the semi-perimeter is, s = (a + b + c)/2 = (10 + 15 + 18)/2 = 21.5. We will find the area of the triangle using Heron's formula.
A = √[s(s-a)(s-b)(s-c)]
= √[8(21. 5-10)(21.5 -15)(21. 5-18)]
= √[21.5 × 11.5 × 6.5 × 3.5]
= √(5625)
≈ 7.5
If 5x + 1 = 21 then x =
Answer:
X would equal 4
Step-by-step explanation:
5 x 4 is 20. And the equation was 5x + 1 = 21.
So, the answer would equal 20. Hope this helped!! :D
Answer:
x=4
Step-by-step explanation:
Start with your equation: 5x+1=21
Subtract 1 on both sides: 5x=20
Divide by 5 on both sides: x=4
Hope I helped
A 2-mile walking trail has a distance marker every 1\4 mile. How many markers are along the trail?
Answer: 8
Step-by-step explanation:
From the question, we are informed that a 2-mile walking trail has a distance marker every 1\4 mile. Hl
The number of markers that are along the trail will be calculated as:
= Length of walking trail / interval of distance marker
= 2 ÷ 1/4
= 2 × 4
= 8
There are 8 markers along the trail.
What is the volume of a rectangular prism with a length of 2.5 cm, a width of 3.1 cm and a height of 1.2 cm?
A. 7.75 cm³
B. 8.1 cm³
C. 8.3 cm³
D. 9.3 cm³
How many words can be formed from the letters of the word 'ENGLISH' ? How many these do not begin with E? How many of these begin with E and do not end with H?
Total Number of words made out of English = 93
The area of the square is
........ square centimeters.
9.5 cm
9.5 cm
Let f(x)=x^2+2 and g(x)=1-3x Find each function value. f(g(-1))
Answer:
78
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
(x^2+2)*(1-3x)=-3x^3+x^2-6x+2
now plug in -1
-3(-1)^3+(-1)^2-6(-1)+2=12
hope this helped
Fill in the blank. The solution to 2 x - 2 + 5 = 13 is ______
Ruth buys 19 identical tickets for £280.25.
Estimate the cost of one ticket.
Answer:
The cost of one ticket is $14.75
Step-by-step explanation:
To find the cost of one ticket we need to divide 280.25 by 19
=$14.75
plz mark me as brainliest
Answer:
The cost of one ticket is $14.75
Step-by-step explanation:
The cost of one ticket is $14.75
To find the cost of one ticket we need to divide 280.25 by 19
=$14.75
please mark as brainliest
Find the Are of the Shaded Region
Answer:
≈ 84.8 cm²
Step-by-step explanation:
The area of the shaded region is calculated as
area of circle - area of unshaded sector
area of circle = πr² = π × 6² = 36π
unshaded area = area of circle × fraction of circle
= 36π × [tex]\frac{90}{360}[/tex] = 36π × [tex]\frac{1}{4}[/tex] = 9π
area of shaded region = 36π - 9π = 27π ≈ 84.8 cm² ( nearest tenth )
PLEASE HELP ME ON THIS QUESTION ASAP!!!! NO LINKS
Answer:
4π in.
Step-by-step explanation:
formula circumference= 2πr
r = half of diameter
How many tiles will figure 13 have ??
FREE POINTS!
Answer:
more tiles than i laid in ur momms
Step-by-step explanation:
Figure 13 has 11 tiles
you throw a basketball from a height of 4 feet with an upward velocity of 15 feet per second the function h=-16t^2+15t+4 gives the height of the basketball after t seconds when does the basket ball hit the floor round your answer to the nearest tenth
Answer:
After 1.2 seconds
Thomas is opening a savings account. Which integer represents his possible balance after making a deposit
A -10
B-5
C 0
D 10
Find the distance between the pair of points (-6.-17) and (-8.-19) The distance is (Round to the nearest thousandth as needed.)
Answer:
2.83
Step-by-step explanation:
d= Square root of (x2 - x1 )^2 +( y2- y1)^2
from the point given you
x1= -6
y1 = -17
x2 = -8
y2 = -19
by applying the formula
Square root of ( -8 - (-6))^2 + ( -19 - (-17))^2
Square root of (-8+6) + (-19+17)^2
helppp! I literally can’t find anything in Brainly I’m dead failing does someone at le
Answer:
C
Step-by-step explanation:
volume of a cone = πr²[tex]\frac{h}{3}[/tex]
so 20² x π x [tex]\frac{35}{3}[/tex] = 14660.76572
What is the difference between 2386 and 7000 check your answer using inverse operations
Answer:
7,000 - 2,386 = 4,614
can someone help me please I don’t understand
Answer:
answer is 3.144
Step-by-step explanation: