Four transformations of the Function f(x)=2^x are given below.
For each transformation drag the expression that shows the result of that transformation to the box under it.
Answers
After applying operations between functions, we find the following four transformations for the function [tex]f(x) = 2^{x}[/tex]:
a) 6 · f(x) - [tex]g(x) = 6 \cdot 2^{x}[/tex]
b) f(6 · x) - [tex]g(x) = 2^{6\cdot x}[/tex]/[tex]g(x) = 2^{6}\cdot f(x)[/tex]
c) f(x + 6) - [tex]g(x) = 2^{x+6}[/tex]/[tex]g(x) = 2^{6}\cdot f(x)[/tex]
d) f(x) + 6 - [tex]g(x) = 2^{x}+6[/tex]
How to determine the transformations of a function
Mathematically speaking, transformations are operations applied on a function such that its domain or range are altered. There are five operations for functions:
AdditionSubtractionMultiplicationDivisionCompositionLet suppose that [tex]f(x) = 2^{x}[/tex], the images of this function are, respectively:
a) 6 · f(x) - Multiplication between two functions
[tex]g(x) = 6 \cdot 2^{x}[/tex]
b) f(6 · x) - Composition between two functions
[tex]g(x) = 2^{6\cdot x}[/tex]
[tex]g(x) = (2^{x})^{6}[/tex]
[tex]g(x) = (f(x))^{6}[/tex]
c) f(x + 6) - Composition between two functions
[tex]g(x) = 2^{x+6}[/tex]
[tex]g(x) = 2^{x}\cdot 2^{6}[/tex]
[tex]g(x) = 2^{6}\cdot 2^{x}[/tex]
[tex]g(x) = 2^{6}\cdot f(x)[/tex]
d) f(x) + 6 - Addition between two functions
[tex]g(x) = 2^{x}+6[/tex]
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Related Questions
Describe fully the single transformation that maps a onto triangle b
Answers
The single transformation that maps a onto triangle b is a rotation of 180 degrees across the common vertex of triangles a and b
How to determine the transformation?From the figure, we have the following highlights
Both triangles are congruentBoth triangles have one common vertexBoth triangles meet at a right angle. this implies a 180-degree rotationThe above highlights mean that the single transformation that maps a onto triangle b is a rotation of 180 degrees across the common vertex of triangles a and b
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Don't worry about the x and w, I just need the answer to y. Find the value of y if JKLM~PQRS
Answers
Answer:
y = 15
Step-by-step explanation:
JKLM ~ PQRS means that quadrilateral JKLM is similar to quadrilateral PQRS.
In similar shapes the corresponding sides have same ratio and the corresponding angles are congruent.
This means angle J is congruent to angle P, K is congruent to Q, L is congruent to R and M is congruent to S. Order of the vertices matters.
Solving for y.
Angle J is congruent to angle P.
5y - 4 = 71 Add 4 on both sides.
5y = 71 + 4
5y = 75 Divide both sides with 5.
y = 15
(Btw your solution for x is wrong.)
HELP ASAP PLEASEEE!!!!!!!!!
Answers
Answer:
all the answer choices are correct
Step-by-step explanation:
reflections & rotations dont change any of the angle measures
Find the domain for each expression:
1. 1/x
2. 1/x+5
3. X+5/x+5
4. X^2/x
5. 7/x-2
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2. X<0 or x>0
3. X<0 or x>0
4. X<0 or x>0
5. X<2 or x>2
3/5 x 3/5
PLEASE SHOW YOUR WORK IT REALLY HELPS :)
Answers
Answer:
9/25
Step-by-step explanation:
3x3 is 9 and 5x5 is 25 so that would equal to 9/25
Answer:
9/25
Step-by-step explanation:
first you do 3x3=9
5x5
9
5x5=25
9/25 is your answer :)
distance between 2 points maze amazing mathematics answer key
Answers
Find the y-intercept of the line on the graph.
Enter the correct answer.
Answers
Check the picture below.
What is the value of x when 1/4x=14 3/4 ?
Answers
Answer:
x = 59
Step-by-step explanation:
[tex]\frac{1}{4}[/tex] x = 14 [tex]\frac{3}{4}[/tex] ← convert to improper fraction
[tex]\frac{1}{4}[/tex] x = [tex]\frac{59}{4}[/tex] ( multiply both sides by 4 to clear the fractions )
x = 59
3 out of 60 is what percent?
Answers
Answer:
5% is the percetange for 3 out of 60
Answer:
5%
Step-by-step explanation:
you know 10% of 60 is 6. 3 is half of 6, and 5% is half of 10
I hope this helps and have a wonderful day :)
Write and solve an addition or subtraction equation to find the missing angle measure
Answers
Answer:
n + 50 = 90; n = 40
Step-by-step explanation:
the angle is a right angle so it adds up to 50
one side is 50
so
n + 50 = 90
subtract 50 to both sides
n = 40
Please Help I Don't Understand!
Answers
Answer:
A. 4.
Step-by-step explanation:
The scale factor is 4.
If you multiply 8, 5, and 2 by 4, you get 32, 20, and 8.
A researcher is interested in whether using mental imagery can help people remember specific details when given information. To conduct the experiment, the researcher asks 100 volunteers to participate. The researcher places everyone’s name in a hat and randomly selects 50 names, making sure to sure to mix the names between each selection.
Which component is missing from the researcher’s process?
The researcher did not use enough randomization in the process.
The researcher used volunteers instead of randomly selected people from the population.
The researcher did not assign the 50 names to the treatment group or the control group.
The researcher should have used numbers instead of names for confidentiality reasons.
Answers
The researcher ought to have divided the volunteers into two groups; the treatment group and the control group at random.
What is scientific method?The scientific method must include the tools of observation, experimentation and conclusion.
In this case, the researcher ought to have divided the volunteers into two groups; the treatment group and the control group at random.
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Please help me it would mean a lot
Answers
Answer:
44 degrees
Step-by-step explanation:
angle c = 90 degrees
angle a = 46 degrees
the measure of all sides on a triangle is 180
so to solve for the other side we can do this equation...
180 - (90 + 46) = 44
hope this helped, mark as brainliest pls
PLEASE HURRY I NEED HELP!!!!
f(x)=x^2. what is g(x)?
A. g(x)= 3x^2
B. g(x)= (1/3x)^2
C. g(x)= 1/3x^2
D. g(x)= 1/9x^2
Answers
Answer:
See Down Here
Step-by-step explanation:
We want to get g(x) given that we know f(x) and the graphs for both functions. We will see that the correct option is D:
g(x) = (x/3)^2
By looking at the graph we can see that f(x) and g(x) are two quadratic functions, and g(x) is just a dilation of f(x).
This means that:
g(x) = A*f(x)
Where A is a real number.
We know that:
f(x) = x^2
And by looking at the graph, we also know that g(3) = 1.
Then we can write:
g(3) = A*f(3) = A*3^2 = 1
Now we can solve this for A:
A*3^2 = 1
A*9 = 1
A = 1/9
Then we have:
g(x) = (1/9)*f(x) = (1/9)*x^2 = (x/3)^2
So the correct option is D.
If you want to learn more about quadratic equations, you can read:
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Lan make 60 cakes. he gives 1/4 of the cakes to Helen. he gives 20 of the 60 cakes to sue. what fraction of the 60 cakes does he have left?
Answers
Answer:
5/12
Step-by-step explanation:
1/4 × 60 = 15
He gave 15 cakes to Helen.
He gave 20 cakes to Sue.
20 + 15 = 35
He gave away a total of 35 cakes.
60 - 35 = 25
He has 25 cakes left.
fraction = 25/60 = 5/12
Javon is in a 30% tax bracket for his federal income tax. If the amount of money that he paid for federal income tax was $21,000, what was his taxable income?
Answers
Answer:
Step-by-step explanation:
Find the residual values, and use the graphing calculator tool to make a residual plot. A 4-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled given with entries negative 3.5, negative 2.9, negative 1.1, 2.2, 3.4. The third column is labeled predicted with entries negative 1.1, 2, 5.1, 8.2, 1.3. The fourth column is labeled residual value with all entries blank. Does the residual plot show that the line of best fit is appropriate for the data? Yes, the points have no pattern. No, the points are evenly distributed about the x-axis. No, the points are in a linear pattern. Yes, the points are in a curved pattern.
Answers
The best answer from the options that proves that the residual plot shows that the line of best fit is appropriate for the data is: ( Statement 1 ) Yes, because the points have no clear pattern
X Given Predicted Residual value
1 3.5 4.06 -0.56
2 2.3 2.09 0.21
3 1.1 0.12 0.98
4 2.2 -1.85 4.05
5 -4.1 -3.82 -0.28
The residual value is calculated as follows using this formula: ( Given - predicted )
1) ( 3.5 - 4.06 ) = -0.56
2) ( 2.3 - 2.09 ) = 0.21
3) ( 1.1 - 0.12 ) = 0.98
4) (2.2 - (-1.85) = 4.05
5) ( -4.1 - (-3.82) = -0.28
Residual values are the difference between the given values and the predicted values in a given data set and the residual plot is used to represent these values .
attached below is the residual plot of the data set
hence we can conclude from the residual plot attached below that the line of best fit is appropriate for the data because the points have no clear pattern ( i.e. scattered )
learn more about residual plots : https://brainly.com/question/16821224
Answer:
A: Yes, because the points have no clear pattern.
Step-by-step explanation:
Edge quiz 100%
Choose the graph that represents the equation y=3[x+1]+1.
Answers
Answer:
Step-by-step explanation:
Discussion
You haven't given us any choices. Always do that it you have them. Look for the graph that looks like the one below. It has the following characteristics
It opens upwardIt lowest point is -1,1y never equals zeroThe y intercept is 0,4Help can you help me with angles please ＞﹏＜
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hope it helps:))
===========================================================
Explanation:
There are two approaches here.
Method 1
Focus on the numbers along the top only.
The left arrow points at 50 while the arrow on the right points at 180. Subtract these numbers to get 180 - 50 = 130
------------------------------
Method 2
Focus on the numbers along the bottom row this time.
The left arrow points at 130 and the right arrow points at 0
The difference of which is 130 - 0 = 130
Because we're subtracting off 0, it means we can simply look at only one number without having to do any math. This only works if the other portion of the angle is pointing at 0 or 180.
------------------------------
Notice that 130 degrees is larger than 90, so this angle is obtuse. This means that if you aren't sure whether to go with 50 or 130, it will depend on if it's acute or obtuse.
Find the equation of the line that
is parallel to y = -5x – 9 and
contains the point (-3, -3).
=
-
y = [? ]X + [ ]
Answers
Answer:
see photo attached for detailed information
Step-by-step explanation:
best answer gets brainly ^^ !!
Answers
Answer:
(6, 0)
Step-by-step explanation:
Coordinates are written in the form (x, y), where x is the x-axis value that the point is in, in this case 6, and where y is the y-axis value, in this case 0.
Hi!
Answer:
(6, 0)
Step-by-step explanation:
Coordinate point "G" on this graph is on the very bottom. On the X axis, point G is on the 6. On the Y axis, its on the 0, so since the domain, (X) comes first before the range, (Y), you get (6, 0)
I hope this helped! Have a wonderful day! :)
(Please someone help me!) (No links!)
What do I put?
Answers
<m(lkj)+<m(ghi)=180°
34°+<m(ghi)=180°
180°-34°=<m(ghi)
146°=<m(ghi)
1. Solve the following formulas
a. Solve the formula 8x + y = 15 for y.
b. Solve the formula 9x + y = 13 for y.
c. Solve the formula −4x + y = − 6 for y.
d. Solve the formula −5x + y = − 1 for y.
Answers
[tex]\textbf{a)}\\\\~~~~~~8x+y = 15\\\\\implies y = 15-8x\\\\\textbf{b)}\\\\~~~~~~9x+y = 13\\\\\implies y = 13 -9x\\\\\textbf{c)}\\\\~~~~~-4x+y = -6 \\\\\implies y = 4x -6 \\\\\textbf{d)}\\\\~~~~~-5x +y = -1\\\\\implies y = 5x -1[/tex]
Step-by-step explanation:
1. 8x+y=15
y=15-8x
2. 9x+y=13
y=13-9x
3. -4x+y=-6
y=4x-6
4. -5x+y=-1
y=5x-1
- The spinner shown is spun 4 times. What is the probability that you will spin gray at least 2 times?
Answers
Answer:
26.17%
Step-by-step explanation:
P(Grey) = 1/4
P(Grey at least 2 times in 4) = 1 - P(no Grey in 4) - P(1 Grey in 4)
P(no Grey in 4) = 4C0 * 3/4 * 3/4 * 3/4 * 3/4 = 81/256
P(1 Grey in 4) = 4C1 * 1/4 * 3/4 * 3/4 * 3/4 = 27/64
P(Grey at least 2 times in 4) = 1 - 81/256 - 27/64 = (256-81-108)/256=67/256=26.17%
If Willie does this (equation in image) correctly, what is the value of k?
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Quadratic equation has a leading degrees of 2. The correct equation in vertex form is (x - 3)^2 + 5
Vertex form of a quadratic equationQuadratic equation has a leading degrees of 2.
Given the quadratic function expressed as:
f(x) = x^2 - 6x + 14
Complete the square
x^2 - 6x + (-3)^2 - (-3)^2 + 14
(x- 3)^2 - 9 + 14
(x - 3)^2 + 5
Hence the correct equation in vertex form is (x - 3)^2 + 5
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wants to buy a CD player for $49.99. She has $20. Which inequality shows how much more money, M, Sally must save?
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This is easy I swear but pls help
Answers
Angle one and two lie on straight line.
this means there sum is equal to 180°
Given :-
angle 1 = 7x angle 2 = x+12so we can say :-
[tex] \angle1 + \angle2 = 180 \degree \\ 7x + x + 12 = 180 \\ 8x + 12 = 180 \\ 8x = 180 - 12 \\ 8x = 168 \\ x = \frac{ \cancel{168} {}^{ \: \: 21} }{ \cancel8} \\ x = 21 \degree[/tex]
so angle one = 7x= 7×21 = 147°
angle two = x+12 = 21+12 = 33°
There are 90 girls and 60 boys in the 6th grade at a middle school. Of these students, 9 girls and 3 boys write left-headed. What percentage of the 6th graders at this middle school write left handed
Answers
Answer:
8%
Step-by-step explanation:
9+3=12 (total number of students that write left handed)
90+60=150 (total number of 6th graders)
12/150 x 100% = 8%
2(6x4) + 2(6x2.4n) + 2(4x2.4n) what is the value of n
Answers
Hey there!
2(6 * 4) + 2(6 * 2.4n) + 2(4 * 2.4n)
= 2(24) + 2(14.4n) + 2(9.6n)
= 48 + 28.8n + 19.2n
= 48 + 48n
= 48n + 48
Thus, your answer should be: 48n
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Solve the following inequality for x. -5x < -15x + 40 a. x > -2.00 b. x > 4 c. x < 4 d. x < -2.00
Answers
Answer:
c. x < 4
Step-by-step explanation:
-5x < -15x + 40
bring -15x to the left to combine like terms
-5x +15x < -15x + 15x + 40
10x < 40
divided both sides by 10 to get x alone
10x / 10 < 40 / 10
x < 4