Graph the function g(x) = 3^x + 3 and give its domain and range using interval notation
Answers
The question is an illustration of a function using graphs. When a function is plotted on a graph, the x-axis represents the domain, while the y-axis represents the range of the function.
The domain and the range of the given function are:
Domain: [tex](-\infty,\infty)[/tex]
Range: [tex](3,\infty)[/tex]
From the question, we have the function to be:
[tex]g(x) = 3^x + 3[/tex]
First, we plot the graph of g(x)
To do this, we first generate values for x and g(x). The table is generated as follows:
[tex]x = 0 \to g(0) = 3^0 + 3 = 4[/tex]
[tex]x = 1 \to g(1) = 3^1 + 3 = 6[/tex]
[tex]x = 2 \to g(2) = 3^2 + 3 = 12[/tex]
[tex]x = 3 \to g(3) = 3^3 + 3 = 30[/tex]
[tex]x = 4 \to g(4) = 3^4 + 3 = 84[/tex]
In a tabular form, we have the following pair of values
[tex]\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ g(x) & {4} & {6} & {12} & {30} & {84} \ \end{array}[/tex]
See attachment for graph
From the attached graph of g(x), we can observe that the curve stretches through the x-axis and there are no visible endpoints.
This means that the curve starts from - infinity to +infinity
Hence, the domain is: [tex](-\infty,\infty)[/tex]
Also, from the same graph, we can observe that the curve of g(x) starts at y = 3 on the y-axis and the curve faces upward direction.
This means that the curve of g(x) is greater than 3 on the y-axis.
Hence, the range is: [tex](3,\infty)[/tex]
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Related Questions
Rate of change or rate of change
A farmer has 80 feet of wire mesh to surround a rectangular pen.
A) Express the area A of the pen as a function of x, also draw the figure of A indicating the admissible values of x for this problem.
B) What are the dimensions of the maximum area pen?
Answers
Answer:
Step-by-step explanation:
A). Let the dimensions of the rectangular pen are,
Length = l
Width = x
Since, farmer has the wire measuring 80 feet to surround the the pen.
Perimeter of the pen = 80 feet
2(l + x) = 80
l + x = 40
l = 40 - x ------(1)
Area of the rectangular pen = Length × width
= lx
By substituting the value of l from equation (1),
Area (A) of the pen will be modeled by the expression,
A = (40 - x)
A = 40x - x²
B). For maximum area of the pen,
Derivative of the area = 0
[tex]\frac{d}{dx}(A)=0[/tex]
[tex]\frac{d}{dx}(A)=\frac{d}{dx}(40x-x^2)[/tex]
= 40 - 2x
And (40 - 2x) = 0
x = 20
Therefore, width of the pen = 20 feet
And length of the pen = 40 - 20
= 20 feet
Dimensions of the pen should be 20 feet by 20 feet.
If a right circular cone is intersected by a plane only at its vertex, as in the
picture below, what shape is produced?
A. A parabola
B. An ellipse
C. A point
D. A line
E. A circle
F. A hyperbola
Answers
Answer:
A point
Step-by-step explanation:
Hopefully this helps :)
If a right circular cone is intersected by a plane passing through its vertex and perpendicular to its base, the resulting shape is a point.
What is mean by cone?A cone is a three-dimensional geometric form with a flat base and a smooth, tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that link the base's points to the apex, which is a common point on a plane that does not include the base.
Now, If a right circular cone is intersected by a plane passing through its vertex and perpendicular to its base, the resulting shape is a point.
Since, This is because a plane passing through the vertex of a cone and perpendicular to its base intersects the cone at only one point, which is the vertex of the cone.
Alternatively, if the plane intersects the base of the cone at any other point than the center, the resulting shape would be a triangle.
Therefore, the required form is a point.
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cho f(x)= sign x và g(x) = x(1-x^2). tìm f(g(x))
Answers
Answer:
[tex]f(g(x))= sign(x(1-x^{2})) = sign(x-x^{3})[/tex]
Step-by-step explanation:
A researcher surveyed 8 people to see if there is a
relationship between years of education and starting
salaries. The data points are shown on the graph.
Which best represents the equation of the trend line
shown on the graph? (Note that the graph has a break
on the x-axis.)
O y = 0.25x + 15
O y = 0.25x + 17.5
* y = 1.25x - 10
O y = 1.25x + 7.5
Answers
Answer:
[tex]y=1.25x+7.5[/tex]
Step-by-step explanation:
We can see that the trend line is the line of best fit to the data points.
The equation of a straight line is given by:
y = mx + b:
where y, x are variables, m is the slope of the line and b is the y intercept.
From the graph, we can see that the line passes through the points (10, 20) and (14, 25). Therefore the equation of the line is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-20=\frac{25-20}{14-10}(x-10)\\\\y-20=1.25(x -10)\\\\y-20=1.25x-12.5\\\\y=1.25x+7.5[/tex]
Jean threw a disc in the air. The height of the disc can be modelled by the function
h = -5t^2 + 31.5t + 2, where h is the height in metres after t seconds.
Patrick fired a paintball at the disc. The path of the paintball is modelled by the function h = 30t + 1, with the same units. How long will it take the paint ball to hit the disc?
Answers
Answer:
It will take 0.62 seconds for the paint ball to hit the disc.
Step-by-step explanation:
Height of the disk:
[tex]H_d = -5t^2 + 31.5t + 2[/tex]
Height of the paintball:
[tex]H_p = 30t + 1[/tex]
When the paintball will hit the disk?
When they are at the same height, so:
[tex]H_d = H_p[/tex]
[tex]-5t^2 + 31.5t + 2 = 30t + 1[/tex]
[tex]5t^2 - 1.5t - 1 = 0[/tex]
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
In this question:
Quadratic equation with [tex]a = 5, b = -1.5, c = -1[/tex]
So
[tex]\Delta = (-1.5)^2 - 4(5)(-1) = 22.25[/tex]
[tex]t_{1} = \frac{-(-1.5) + \sqrt{22.25}}{2(5)} = 0.62[/tex]
[tex]t_{2} = \frac{-(-1.5) - \sqrt{22.25}}{2(5)} = -0.32[/tex]
Time is a positive measure, so 0.62.
It will take 0.62 seconds for the paint ball to hit the disc.
The following data represents the age of 30 lottery winners.
22 30 30 35 36 37 37
37 39 39 41 51 51 54
54 55 57 57 58 58 61
64 68 69 72 74 75 78 79 80
Complete the frequency distribution for the data.
Age Frequency
20-29
30-39
40-49
50-59
60-69
70-79
80-89
Answers
20-29 ==> 1
30-39 ==> 9
40-49 ==> 1
50-59 ==> 9
60-69 ==> 4
70-79 ==> 5
80-89 ==> 1
(Total 30)
what 30 + 30+60+(56)-82=?
Answers
94 is the correct answer for that question
Step-by-step explanation:
30+30+60+56-82=94
A rope is 56 in length and must be cut into two pieces. If one piece must be six times as long as the other, find the length of each piece. Round your answers to the nearest inch, if necessary.
Answers
Answer:
48, 6
Step-by-step explanation:
The ratio of the pieces is 6 to 1
Add them together to get the total
6+1 = 7
Divide the total length by 7
56/7 = 8
Multiply the ratios by 8
6*8 = 48
1*8 = 6
The peices are 48 and 6
Help please!! Based on Pythagorean identities, which equation is true ??
Answers
Answer:
Last answer: [tex]cot^{2} \alpha - csc^{2} \alpha = -1[/tex]
sorry couldn't find theata so I just used alpha.
Hshejoffpeowhwbwbwhjskfofofoekwwoksnfnf Helppp
Answers
Answer:
Step-by-step explanation:
3. ZW ≅ WX
Which of the following statements are true?
A. Both graphs are exponential functions.
B. Both graphs are logarithmic functions.
C. Both graphs have exactly one asymptote.
D. Both graphs have been shifted and flipped.
Answers
Answer:
A, C, and D are the answers to this question
The true statements about the graphs are; A. Both graphs are exponential functions. C. Both graphs have exactly one asymptote. D. Both graphs have been shifted and flipped.
How to Interpret Function Graphs?The graphs are exponential functions because as x increases, the value of y approaches infinity.
Likewise the graphs have exactly one asymptote.
Lastly, we can see that both graphs appear to have been shifted and flipped especially when we look at their respective coordinates.
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If all possible random samples of size N are drawn from a population with a mean of mu and a standard deviation of sigma, then as N becomes larger, the sampling distribution of sample means becomes approximately normal with a mean of muy(bar) and a standard deviation of sigmay(bar). This statement is known as the:
Answers
Answer:
"Central limit theorem" is the right answer.
Step-by-step explanation:
A hypothesis essentially claims that whenever there seems to be a small variance throughout the big confidence intervals, the sampling is based on averages as well as the sampling distribution (mean) usually nearly the same as the public's median.
When,
Mean = [tex]\mu_y[/tex]Standard deviation = [tex]\sigma_y[/tex]Sample size = Nis sufficiently larger than [tex]\bar Y \sim N(\mu_y, \sigma_y)[/tex]
Thus, the above is the right answer.
Suppose you make napkin rings by drilling holes with different diameters through two wooden balls (which also have different diameters). You discover that both napkin rings have the same height 5h. Use cylindrical shells to compute the volume V of a napkin ring of height 5 h created by drilling a hole with radius r through the center of a sphere of radius R and express the answer in terms of h .
Answers
Answer:
V = 1/6 π ( 5h)^3
Step-by-step explanation:
Height of napkin rings = 5h
Compute the volume V of a napkin ring
let a = 5
radius = r
express answer in terms of h
attached below is the detailed solution
What’s the equation?
Answers
Answer:
The answer is D.
Step-by-step explanation:
Find the missing length indicated
Answers
Answer:
x = 175
Step-by-step explanation:
Please help on this initial amount problem
Answers
Growth
Value of car change 28% each year
How would yo expand ln (1/49k)?
Answers
Answer:
Step-by-step explanation:
It depends on whether you mean ln(1/49k) or ln(1/(49k)).
Help solve problem please
Answers
Answer:
1 / 13
Step-by-step explanation:
The total number of cards in a deck = 52
The total number of aces in a deck = 4
Since selection is drawn with replacement, then probability of drawing a certiaj number of card from the deck will be the same each time a selection is made :
Probability = required outcome / Total possible outcomes
The required outcome = number of aces = 4
Total possible outcomes = total number of cards = 52
P(drawing an ace) = 4 / 52 = 1 /13
Two real estate companies, Century 21 and RE/MAX, compete with one another in a local market. The manager of the Century 21 office would like to advertise that homes listed with RE/MAX average more than 10 days on the market when compared to homes listed with his company. The following data shows the sample size and average number of days on the market for the two companies along with the population standard deviations.Sample mean Sample size Population standard deviation Century 21 22 days 36 32 days RE/MAX 144 days 30 35 daysIf Population 1 is defined as RE/MAX and Population 2 is defined as Century 21, the 80% confidence interval for the difference in population means is:_________.(17.8, 26.2)(11.5, 32.7)(5.4, 38.6)(-3.0, 47.0)
Answers
Answer:
17.8 , 26.2
Step-by-step explanation:
The confidence interval is 80% for the given population. Significance level is 0.2 [ 1 - 0.8 ] . Sample size is given and sample mean is calculated with the given standard deviation. Sample mean is 36 days and population size is 144 days.
When a fridge is imported, a customs value of 10% must be paid for its value. If the value of the fridge after paying the customs value is rs. 55,000/-. What is the value before paying customs duty?
Answers
Answer:
55000×100/90
61,111.111
Game consoles: A poll surveyed 341 video gamers, and 95 of them said that they prefer playing games on a console, rather than a computer or hand-held device. An executive at a game console manufacturing company claims that the proportion of gamers who prefer consoles differs from . Does the poll provide convincing evidence that the claim is true
Answers
Answer:
proportion of gamers who prefer console does not differ from 29%
Step-by-step explanation:
Given :
n = 341 ; x = 95 ; Phat = x / n = 95/341 = 0.279
H0 : p = 0.29
H1 : p ≠ 0.29
The test statistic :
T = (phat - p) ÷ √[(p(1 - p)) / n]
T = (0.279 - 0.29) ÷ √[(0.29(1 - 0.29)) / 341]
T = (-0.011) ÷ √[(0.29 * 0.71) / 341]
T = -0.011 ÷ 0.0245725
T = - 0.4476532
Using the Pvalue calculator from test statistic score :
df = 341 - 1 = 340
Pvalue(-0.447, 340) ; two tailed = 0.654
At α = 0.01
Pvalue > α ; We fail to reject the null and conclude that there is no significant evidence that proportion of gamers who prefer console differs from 29%
help help me please!!!!!!!
Answers
9514 1404 393
Answer:
a) 3092.5 (rounded to tenths)
b) 39,600
c) ₹28,755
Step-by-step explanation:
These are all simple calculator problems. The arithmetic involved is something you learned in 2nd or 3rd grade.
__
a) Since we divide using the division algorithm, it isn't clear what "check your answer by division algorithm" is intended to mean. The result of the division (stopping at 1 decimal place) is 3092.5.
The usual method of checking a division problem is to multiply the quotient by the divisor to see if the dividend value is the result. Here, we have ...
13×3092.5 = 40202.5
This differs by from the dividend of 40203 by 0.5, which is the remainder showing in our long division. In short, the answer checks OK.
__
b) The value of each 4 is found by setting other digits to 0.
Most significant 4: 40,000
Least significant 4: 400
Difference in place value: 40,000 -400 = 39,600
__
c) The balance in the account is found by subtracting withdrawals from deposits:
₹35000 -6245 = ₹28,755
How do you do this I’ve been stuck on this
Answers
9514 1404 393
Answer:
x^(1/6)
Step-by-step explanation:
The applicable rule of exponents is ...
(a^b)/(a^c) = a^(b-c)
__
Here, we have a=X, b=1/2, c=1/3, so the quotient is ...
(X^(1/2))/(X^(1/3)) = X^(1/2 -1/3) = X^(1/6)
_____
Expressed as a radical, this is ...
[tex]\displaystyle X^{\frac{1}{6}}=\sqrt[6]{X}[/tex]
Answer:
Step-by-step explanation:
x^1/2÷x^1/3=(x)^1/2-1/3= x^1/6--->⁶√x...it's positive answer.
Which expression is equivalent to 9+y+y+3
Answers
Answer:
b
Step-by-step explanation:
You only need to add the real numbers and the ys.
Answer:
12 + 2y
Step-by-step explanation:
9+y+y+3
Combine like terms
9+3 + y+y
12 + 2y
What is circulatry systerm
Answers
Answer: i think you meant circulatory system but the defination for it is:
The circulatory system (also called the cardiovascular system) is the body system that moves blood around the body. It consists of the heart and blood vessels. The blood carries various materials that the body needs, and takes away waste or harmful substances. Blood vessels that take blood away from the heart are arteries.
If 800g of a radioactive substance are present initially and 8 years later only 450g remain, how much of the substance will be present after 16 years? (Round answer to a whole number)
Answers
A=Pe^(rt)
P = 800g
t = 8 years
A = 450g
r = This is what we will try and find to start with
450=800e^(r*8)
After running the math through a calculator, we end with r = -0.07192
Now we just re-input this information into our equation: A=800e^(-0.07192*16)
A=800e^(1.15072)
Now we will re-write the equation using the negative exponent rule:
A = 800 1/e^1.15072
Combine right side:
A = 800/e^1.15072
Then do the math:
A = 253.12709836......
That will give us A = 253 (rounded to the whole number)
I hope this helps! :)
The substance that should be presented after 16 years is 253.
Given that,
If 800g of a radioactive substance are present initially and 8 years later only 450g remain.Based on the above information, the calculation is as follows:
We know that
[tex]A=Pe^{rt}[/tex]
Here
P = 800g
t = 8 years
A = 450g
[tex]450=800e^{r\times 8}\\\\A=800e^{-0.07192\times 16}\\\\A=800e^{1.15072}\\\\A = 800 \ 1 \div e^{1.15072}\\\\A = 800\div e^{1.15072}[/tex]
A = 253
Therefore we can conclude that the substance that should be presented after 16 years is 253.
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find x in this similar triangles
Answers
Answer:
6. x = 4
8. x = 13
Step-by-step explanation:
Using similar triangles theorem,
6. (5+4)/5 = (4x + 2)/(4x + 2 - 8)
9/5 = (4x + 2)/(4x - 6)
Cross multiply
9(4x - 6) = 5(4x + 2)
36x - 54 = 20x + 10
Collect like terms
36x - 20x = 54 + 10
16x = 64
16x/16 = 64/16
x = 4
8. (4x + 13)/20 = 52/16
(4x + 13)/20 = 13/4
Cross multiply
4(4x + 13) = 13(20)
16x + 52 = 260
16x = 260 - 52
16x = 208
x = 208/16
x = 13
4. In SI, motor output is rated in
A. horsepower.
B. newtons.
C.foot-pounds per second.
D. kilowatts.
Answers
Answer:
in so in Newton motor out put is rate
what is the value of tan 0 in the unit circle below
Answers
Tangent = opposite / adjacent, or in this case Tangent = y / x.
Tan = (1/2) / ([tex]\sqrt{3}[/tex] / 2)
1 / [tex]\sqrt{3}[/tex]
[tex]\sqrt{3}[/tex] / 3
Hope this helps!
PLEASE HELP I REALLY NEED THIS
How is an inequality different from an equation?
What are four ways inequality can be written?
What would the graph of each inequality look like on a number line? (use an example)
What would the graph of an equation look like on a number line(use an example)
Pam has 15 candies in a jar, her sister threw in some more ( the ones she doesn’t like) and now Pam has 27. Write an equation to determine how many candies ( x) her sister put in the jar. Solve using both inverse operations and a balance scale.
Explain the Golden Rule for solving equations
using an example.
What does it mean if a situation has a condition or constraint? Give an example.
Give an example of a situation that contains an independent and dependent variable. Explain if your data is continuous or discrete.
Answers
Answer:
inequality is mostly represented on a number line but equation is not.
