Answers
Answer:
Parent function
[tex]f(x)=\log_2(x)[/tex]
Since we cannot take logs of zero or negative numbers, the domain is [tex](0, \infty)[/tex] and there is a vertical asymptote at [tex]x=0[/tex].
There are no horizontal asymptotes and the range is [tex](- \infty,\infty)[/tex].
The end behaviors of the parent function are:
[tex]\textsf{As } x \rightarrow 0^+, f(x) \rightarrow - \infty[/tex]
[tex]\textsf{As } x \rightarrow \infty, f(x) \rightarrow \infty[/tex]
To determine the attributes of the given function, compare the given function with the parent function.
Given function
[tex]f(x)=- \log_2(x)+5[/tex]
The given function is reflected in the x-axis. Therefore, the end behaviors are a reflection of those of the parent function:
[tex]\textsf{As } x \rightarrow 0^+, f(x) \rightarrow \infty[/tex]
[tex]\textsf{As } x \rightarrow \infty, f(x) \rightarrow - \infty[/tex]
As the given function is translated vertically (5 units up) only, the domain, range and asymptote will not change, since the function has not been translated horizontally.
[tex]\textsf{Domain}: \quad (0, \infty)[/tex]
[tex]\textsf{Range}: \quad (- \infty, \infty)[/tex]
[tex]\textsf{Asymptote}: \quad x=0[/tex]
Conclusion
The function f(x) is a [tex]\boxed{\sf logarithmic}}[/tex] function with a [tex]\boxed{\sf vertical}}[/tex] asymptote of [tex]\boxed{x = 0}[/tex].
The range of the function is [tex]\boxed{(- \infty, \infty)}[/tex], and it is [tex]\boxed{\sf decreasing}[/tex] on its domain of [tex]\boxed{(0, \infty)}[/tex].
The end behavior on the LEFT side is as [tex]\boxed{x \rightarrow 0^+}[/tex], [tex]\boxed{f(x) \rightarrow \infty}[/tex], and the end behavior of the RIGHT side is [tex]\boxed{x \rightarrow \infty}[/tex], [tex]\boxed{f(x) \rightarrow -\infty}[/tex].
Related Questions
An experiment consists of spinning the spinner shown. All outcomes are equally likely. Find P(>6). Express your answer as a fraction in simplest form. spinner of 8 numbers
Answers
Answer:
[tex]\boxed{\huge{\sf \dfrac{1}{4} }}[/tex]
Explanation:
Given Total Numbers: 8 numbers
Must be greater than 6, The numbers are 7 and 8 = 2 numbers
Probability:
→ favorable outcomes/total possible outcomes
→ 2/8
→ 1/4
→ 0.25
Evaluate the expression if a = 2, b = −3, c = −4, h = 6, y = 4, and z = −1.
|2b−3y||+5z
Answers
Answer:
-23
Step-by-step explanation:
Divide.
653 ÷ 8
81 R 3
81 R 5
82 R 3
82 R 5
Answers
653/8
=81 R 5
Step-by-step explanation:
when you divide 653 by 8 you get 82 reminder 5
to prove try multiplying 82 by 8 you will get 5 as the remainder
what are the zeos of f(x)=(x-1)(x+6)
Answers
The zeroes of the given polynomial is 1 and -6.
What is Polynomials?A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
Here, given equation;
f(x) = (x - 1)(x + 6)
for finding the zeros of the equation we need to put.....f(x) = 0
0 = (x - 1)(x + 6)
x - 1 = 0 or x + 6 = 0
x = 1 or x = -6
Thus, The zeroes of the given polynomial is 1 and -6.
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evaluate
8a-b
if a = 10 and b= 6
Answers
Answer:
74
Step-by-step explanation:
(8x10) - 6 =
80 - 6 = 74
What is the correct expanded from and value of 4^3
Answers
Answer:
4^3 = 4x4x4
Step-by-step explanation:
its just a shortened version of 4x4 3 times
Write a sine function that has an amplitude of 5, a midline of 3 and a period of 6pi/7
Answers
Answer:
y = 5sin(6π/7) + 3
3(x + 4)(x - 5) answer to that
Answers
Answer:
3(x + 4)(x - 5) = 3x² - 3x - 60.
Step-by-step explanation:
3(x + 4)(x - 5)
Combine x + 4 and x - 5 using FOIL, or first, outer, inner, last.
F: x * x = x²
O: x * -5 = -5x
I: x * 4 = 4x
L: 4 * -5 = -20
3(x² - 5x + 4x - 20)
Simplify inside the parenthesis.
3(x² - x - 20)
Distribute the 3 into the equation.
3x² - 3x - 60
Find the mean from the following data:
1, 8, 3, 2, 8, 8
Answers
Answer:
5
Step-by-step explanation:
to find the mean you have to add up all the numbers so
1+8=9
9+3=12
12+2=14
14+8=22
22+8= 30
and then you divide by the amount of numbers which is 30 / 6 = 5
Hope This Helped
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{QUESTION READS}[/tex]
[tex]\large\textsf{Find the mean from the following data:1, 8, 3, 2, 8, 8}}[/tex]
[tex]\huge\textbf{A LITTLE BREAKDOWN OF MEAN}[/tex]
[tex]\large\text{To find the \underline{\underline{mean}} you have to ADD all of the numbers \& DIVIDE}\\\large\text{by the total numbers you have in your data plot..}[/tex]
[tex]\large\text{Here's the formula: }\large\boxed{\rm{\dfrac{the\ sum\ of\ all\ terms}{number\ of\ terms\ you\ have} = your\ \bf mean}}[/tex]
[tex]\huge\textbf{ANSWERING THE QUESTION}[/tex]
[tex]\large\text{Your equation: }\large\boxed{\rm{\dfrac{1 + 8 + 3 + 2 + 8 + 8}{6} = your \ \bf mean}}\\\\\large\boxed{\rm{\dfrac{1 + 8 + 3 + 2 + 8 + 8}{6}}}\\\\\large\boxed{\rm{= \dfrac{9 + 3 + 2 + 8 + 8}{6}}}\\\\\large\boxed{\rm{= \dfrac{12 + 2 + 8 + 8}{6}}}\\\\\large\boxed{\rm{= \dfrac{14 + 8 + 8}{6}}}\\\\\large\boxed{= \rm{\dfrac{22 + 8}{6}}}\\\\\large\boxed{= \rm{\dfrac{30}{6}}}\\\\\large\boxed{\rm{= 5}}[/tex]
[tex]\huge\textbf{MET THE ANSWER OF THE}\\\huge\textbf{QUESTION}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{5}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
2r + 3s = 14
2( )+ 3s = 14
+3s = 14
3s=
S =
Answers
Answer:
4
Step-by-step explanation:
3s=14-2
3s=12
3s/3=12/3
s=4
como simplificar 20/36
Answers
Answer:
5/9
Step-by-step explanation:
20÷36
20/36
divide using 2
10/18
divide using 2
5/9
find the value of z?
Answers
Two number cubes are rolled for two separate events:
Event A is the event that the sum of numbers on both cubes is less than 10.
Event B is the event that the sum of numbers on both cubes is a multiple of 3.
Find the conditional probability of B given that A occurs first.
Enter your answer as a simplified fraction.
Answers
Using it's concept, it is found that the conditional probability of B given that A occurs first is of [tex]p = \frac{3}{10}[/tex].
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
When two dice are rolled, we have these 36 outcomes:
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)Of those, 30 involve a sum of less than 10, and of those 30, 9 involve a sum that is multiple of 3(either 3, 6 or 9), hence the probability is given by:
[tex]p = \frac{9}{30} = \frac{3}{10} = 0.3[/tex]
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(8x^9y^54)^1/3
Simplify the equation
Answers
Answer:
2x^3 y^18
Step-by-step explanation:
The power of a power (properties of exponents) was used in this problem. Hope this helps! :)
Answer:
[tex]2x^3 y^{18}[/tex]
Step-by-step explanation:
[tex]~~~\left( 8 x^9 y^{54} \right)^{\tfrac 13}\\\\=\left(2^3 x^9 y^{54} \right)^{\tfrac 13} \\\\=\left( 2^3 \right)^{\tfrac 13}\left( x^9 \right)^{\tfrac 13}\left( y^{54} \right)^{\tfrac 13}\\\\=2^{\tfrac 33} \cdot x^{\tfrac 93} \cdot y^{\tfrac{54}3}\\\\=2x^3 y^{18}[/tex]
What is the range of the linear relation?
{(0.-6),
(2,-2),
(3.0)}
Answers
Graph f(x) = √x + 2 over the domain - 2 ≤x≤7.
Answers
Answer:
The Graph is included Bellow...
Step-by-step explanation:
This function will start at (0,2) and proceed to the right (based on its family function of √x) and since it has been shifted up 2 from f(x) then we will move two units up.
The domain can be considered the range from right to left that the function is restricted in. In this case, it starts at -2 (Which the function doesn't reach) and will stop at 7.
So the Graph you are looking for will start at (0, 2) and proceed to the right until (7, 4.6) ish. I have included a table to help your graph it!
Please Like if this helps!
a discount of $8.40 on something that usaully costs $28.00.What percent discount was received
Answers
Answer: 30%
Step-by-step explanation:
percentage = (discount/total amount)
* 100= (8.40/28)*100=30%
An outlier is a data value that is numerically distant from most of the other data _______ in a dataset.
Answers
a) If any values in the data set are greater than the upper boundary, then those values are the upper outliers.
b) If any values in the data set are less than the lower boundary, then those values are lower outliers.
The complete question is attached with an answer.
What are Outliers?If a number in distribution is more than 1.5 times the length of the box away from either of the upper and lower quartile of the distribution, then that number is said to be an outlier.
The lower quartile is and the upper quartile of distribution is
Then lower boundary is given by [tex]=Q_1-1.5\times IQR[/tex]
The Upper boundary is given by [tex]=Q_3+1.5\times IQR[/tex]
If any number or value of the distribution is greater than [tex]=Q_3+1.5\times IQR[/tex] then that is called Upper Outlier.
Similarly, if any value or number of the distribution is less than [tex]=Q_1-1.5\times IQR[/tex] then that is called Lower Outlier.
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The diagonals of a trapezoid are 15 cm and 13 cm. The height is 12 cm. Find the area of the trapezoid.
Answers
Answer:
168cmsqured
Step-by-step explanation:
as for me,15 acts as the lower part of the trapezium while 13 acts as the upper part of the trapezium .so since I know the measurements of the both sides I can easily calculate the area use using the formula indicated in the image.hope it helps
whats -6 times 3 over 2
Answers
Answer:
-9
Step-by-step explanation:
-6×3/2
-6×3=-18
-18/2
-9
PLEASE HELP I’LL MAKE YOU THE BRAINIEST!! What is the value of x in simplest radical form
Answers
There are 30 students in a homeroom. How many different ways can they be chosen
to be elected President, Vice President, Treasurer, and Secretary?
Answers
You could vote on it? There are as many ways as you can think of. It’s not set in stone.
Bob's Gift Shop sold 250 cards for Mother's Day. One salesman, Alang, sold 4% of the cards sold for Mother's Day. How many cards did Alang sell?
Answers
Answer:
10 cards
Step-by-step explanation:
4% of 250 cards
(4/100) x 250 cards
10 cards ✔️
Which expression is equivalent to the given expression? Assume the denominator does not equal zero.
Answers
Answer:
A
Step-by-step explanation:
Answer:
[tex]2x^6y^2[/tex]
Step-by-step explanation:
Step 1: simplify integers in expression
[tex]\frac{12x^{9}y^{4}}{6x^{3}y^{2}} = \frac{2x^{9}y^{4}}{x^{3}y^{2}}[/tex]
Step 2: simplify x terms
[tex]\frac{2x^{9}y^{4}}{x^{3}y^{2}} = \frac{2x^{6}y^{4}}{y^{2}}[/tex]
Step 3: simplify y terms
[tex]\frac{2x^{6}y^{4}}{y^{2}} = 2x^6y^2[/tex]
hey guys can you help me with this question love
Answers
Answer: -∞ < x < ∞
Step-by-step explanation:
The domain is all the x-values, or inputs, of a function. The range is the y-values, or outputs, of a function.
In this case, we are looking for the x-values of the function. Since the function will keep going "out forever" in both directions, the answer should be the fourth option;
- ∞ < x < ∞
The first step that we must take to solving this problem is to fully understand what the problem statement is asking from us and what is given us to solve the problem. Looking at the problem statement, we can see that they are asking us to determine what the domain of the function is in the graph that was provided. However, first of all, let us define what domain is.
Domain ⇒ Domain is what x-values can be used in the function that is graphed. For example, if a line just goes side to side all the way to negative and positive infinity, then the domain would be negative infinity to positive infinity as it includes all of the x-values in it's solutions.Looking back at our problem, we can see that this is similar to the example that was provided in the definition. We can see that the parabola reaches out to both positive and negative infinity in the x-direction but at a slope. Although we can only see it reach -2 and 6 we know that the parabola continues going on even after that.
Therefore, looking at the options that were provided option D, -∞ < x < ∞ would be the best fit as it showcases that x reaches from negative infinity to positive infinity.
Which of the following functions is graphed below?
Answers
The option that is the functions is graphed below is known as option A = Y= (x+4) -2.
What is the function about?The function graphed above is Y=|x+4|-2 because when you solve for the graphs, the number in the x-axis is always changed or turned to the other side and there one can see that it would be -4 would be +4, and +4 and also -4.
Note that
Y = (x+4) -2.
x = (0 + 4) - 2
x = 4-2
x =2
Therefore, plug x into the equation.
Y = (x+4) -2.
= ( 2 + 4) - 2
= (6) -2
= 4
Therefore, The option that is the functions is graphed below is known as option A = Y= (x+4) -2.
See full question in the image attached.
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The dimensions of the base of Box 1 are x by 3x.
The base area of Box 1 is:
O 3x
O 3x²
O 3x³
O4x
Answers
Answer:
3x^2
Step-by-step explanation:
Area = (length) x (width)
Area = (1x)*(3x)
Area = 3x^2
simplify the expression
Answers
Answer:
[tex]\sf 10x-2[/tex]Step-by-step explanation:
[tex]\sf \left(2x+\cfrac{1}{2}\right)+\left(8x-2\cfrac{1}{2}\right)[/tex]
We'll need to convert the mixed number 2 1/2 to improper fraction.
[tex]\sf \left(2x+\cfrac{1}{2}\right)+\left(8x-\cfrac{5}{2}\right)[/tex]
Simplify...
[tex]\sf 2x+\cfrac{1}{2}+8x-\cfrac{5}{2}[/tex]
Add similar elements.
[tex]\sf 10x+\cfrac{1}{2}-\cfrac{5}{2}[/tex]
[tex]\sf 10x+\cfrac{-4}{2}[/tex]
Divide numbers..
[tex]\sf 10x-2[/tex]
_______________________
(A) Find the slope of the line that passes through the given points.
(B) Find the standard form of the equation of the line.
(C) Find the slope-intercept form of the equation of the line.
(-3,4) and (6,4)
(A) Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
OA. The slope is m =
(Type an integer or a simplified fraction.)
B. The slope is not defined.
Answers
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{(-3)}}} \implies \cfrac{0}{6 +3}\implies 0[/tex]
hmmm a line with a slope of 0 is a horizontal one, and it has no slope-intercept form.
Check the picture below.
Write the equation of the line in fully simplified slope-intercept form.