We define transformations as operators that act on functions by modifying them in some given way. One type of transformation is a translation, which will move the whole graph of the function in some give direction.
For a general function f(x), we will find that the equation for the result of shifting the graph up by 4 units and left by 2 units is:
g(x) = f(x + 2) + 4
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Let's see how to solve this.
We need to start by defining the two most common translations (also known as shifts).
Horizontal translation:
For a given function f(x), an horizontal translation of N units is written as:
g(x) = f(x + N)
where if N is positive, the translation is to the left.
If N is negative, the translation is to the right.
Vertical translation:
For a given function f(x), a vertical translation of N units is written as:
g(x) = f(x) + N
Where if N is positive, the translation is upwards.
If N is negative, the translation is downwards.
Here for an unknown function f(x), we want to write the equation that gives a shift up of 4 units and left by 2 units.
The shift up of 4 units is written as:
g(x) = f(x) + 4
The shift of 2 units to the left is written as:
g(x) = f(x + 2)
These two together give:
g(x) = f(x + 2) + 4.
This is the equation we wanted to get.
If you want to learn more, you can read:
https://brainly.com/question/24401156
Two numbers have a sum of 24
and a product of 143. What is the
smaller number?
Answer:
The smaller number is 11.
Step-by-step explanation:
11 + 13 = 24
11 x 13 = 143
Hope this helps!
can someone pls help me <33
9514 1404 393
Answer:
(a) 29/69
Step-by-step explanation:
It can help to be familiar with divisibility rules. Even numbers are divisible by 2, so the fraction 174/414 can immediately be reduced to 87/207.
Both numbers have a digit total that is divisible by 3, so each of these numbers can further be divided by 3, reducing the fraction to 29/69. The number 29 is prime, so this fraction cannot be reduced further.
The reduced fraction is ...
made shots/attempts = 174/414 = 29/69
__
Additional comment
As is often the case, a calculator can help you identify arithmetic expressions that have the same value (are equivalent).
174/414 ≈ 0.42028986
29/69 ≈ 0.42028986 . . . . same value
87/207 ≈ 0.42028986 . . . . same value, but 29/69 is reduced
17/41 ≈ 0.41453415 . . . . . not equivalent
14/46 ≈ 0.30434783 . . . .not equivalent (and not reduced; both numbers are even)
I need help please I need to turn it in tomorrow at 8:00 AM
Answer:
The estimate is too low
Step-by-step explanation:
46×6=276 which isn't a very close estimate. However if you used 46×7=322 the estimate would be OK. Now if you used 46×8=368 that would be too high of an estimate here. In simpler terms 1 to 6 is too low of an estimate here and 8 to 9 is too high of an estimate. The number 7 is the middle ground here. Hope this helped.
Write the point slope form of a line that passes through (1,-5) and is perpendicular to a line with a slope of 1
Answer:
y + 5 = -1 (x - 1)
Step-by-step explanation:
y = -1
y + 5 = -1 (x - 1)
How to find the frequency for temperature in Fahrenheit
Answer:
Step-by-step explain
if you where in your house say that your house is set to 72F and you want to find out the Fahrenheit you take the 2 in 72 and multiply it by 3 so in that case it would be 6 then you take the 7 and subtract 1 which makes it 6 So the Fahrenheit is 66.
What is the domain and range
Answer:
The domain is the travel on the x-axis of the graph and the range is the travel on the y-axis of the graph.
Step-by-step explanation:
A triangle has side lengths 35 cm, 46 cm, and 68 cm.
What type of triangle is this?
scalene
isosceles only
equilateral
Answer: Scalene
Step-by-step explanation:
The triangle doesn't have any equal side
Answer:
This is a scalene triangle. Hope this helps.
Determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. x-8=8-x
Hello!
Answer:
One solution (8)
Step-by-step explanation:
Hope this helps!
how do you solve the following equation?
10-s=34
Answer:
-24
Step-by-step explanation:
10-s=34
collect like terms
10-34=s
s=-24
Given f(x) and g(x) = f(x) + k, use the graph to determine the value of k.
Count the boxes each as 1.
Its easier to calculate on y axis.
f(x) intersected at -2g(x) intersected at 3.[tex]\\ \sf\longmapsto k=3-(-2)[/tex]
[tex]\\ \sf\longmapsto k=3+2[/tex]
[tex]\\ \sf\longmapsto k=5[/tex]
Answer:
• For g(x), consinder y-intercept (0, 3)
• For f(x), consinder point y-intercept (0, -2)
[tex] \hookrightarrow \: { \tt{g(x) = f(x) + k}}[/tex]
• substitute using coordinates above:
[tex]{ \tt{3 = - 2 + k}} \\ \\ { \tt{k = 3 + 2}} \\ \\ { \boxed{ \tt{ \: \: k = 5 \: \: }}}[/tex]
Solve each equation 5(-8+5k) +5k=-250
Answer:
k = 7
Step-by-step explanation:
-40+25k +5k = -250
30k = -250 + 40
k = -210/30
k = 7
Robert must read a few books from his home library. He read 4 out of 6 books from the top shelf, 2 out of 3 books from the miidle shelf, and then 3 out of 6 books from the bottom shelf. In how many ways can Robert read the books
Answer:
13
Step-by-step explanation:
I don’t know I did it in my head
Can someone help me solve x?
9514 1404 393
Answer:
x = 1
Step-by-step explanation:
The diagram is intended to show you that the whole is the sum of the part:
11 = (10x -1) +(2x)
11 = 12x -1 . . . . . . . collect terms
12 = 12x . . . . . . . . add 1 to both sides
1 = x . . . . . . . . . . . divide both sides by 12
The value of x is 1. The lengths of the segments are 9 and 2.
Please help me answer this question
Answer:
option D is right answer
i.e. _
BC
What is the value of x and y? Question 6 options: x = 40 , y = 40 x = 8, y = 20 x = 8 , y = 40 x = 40, y = 20
Answer:
the triangle is isosceles triangle. so, the two angles of the same side are equal.
(5x)°=40°
x = 40/5
x = 8
40° +40°+(2y+20)°=180°
80 + 2y +20 =180°
100° +2y =180°
180°-100°=2y
80° = 2y
80°/2= y
40 = y
Please help!!!!!!!!!!!
Answer:
1. x=3
2.x=-14
3.x=13
4.x=-15
5.y=4
Step-by-step explanation:
solve include real and non real solutions.
x^2-8=0
Answer:
[tex]x=+2\sqrt{2} and-2\sqrt{2}[/tex]
Step-by-step explanation:
[tex]x^2-8=0[/tex]
[tex]x^2=8[/tex]
[tex]\sqrt{x^2} = \sqrt{8}[/tex]
[tex]x=2\sqrt{2}[/tex]
plus or minus
Can someone help me please :)
9514 1404 393
Answer:
(d) y = 2×7^x
Step-by-step explanation:
If you try x=2 in each of the expressions, you find only one of the gives 98 as the value.
a) 14^2 = 196
b) 7×2^2 = 28
c) 2^(7×2) = 2^14 = 16,384
d) 2×7^2 = 2×49 = 98 . . . . . . . correct answer choice
__
Alternatively, you can recognize that the x-values in the given (x, y) pairs differ by 1, so the ratio of y-values will be the base of the exponential term:
98/14 = 7
so you're looking for something of the form 7^x. That would be ...
y = 2×7^x
__
In more general terms, consider
y = ab^x
If you have x=1 and x=2, then this will be ...
y1 = ab^1 = ab
y2 = ab^2
Dividing the second by the first gives ...
y2/y1 = (ab^2)/(ab) = b . . . . . . . general solution when x-values differ by 1
98/14 = b = 7
From the x=1 case, we have ...
14 = 7a ⇒ a = 2
y = 2·7^x
Question 6(Multiple Choice Worth 1 points)
(05.03 LC)
What is the initial value of the equation shown?
y = - 4x - 3
0-4
0-3
03
04
The lines given by the equations y = 2x and y= 2x + 1 are
A. Parallel
B. Perpendicular
C. Neither Perpendicular nor parallel
Hi, I really need help on this, please help me, no scam links.
Answer:
560 cm^3
Step-by-step explanation:
To find volume you will have to multiply all three, length, width and height of an object to determine the answer.
In this problem, 7 cm * 20 cm * 4cm = 560 cm^3
Solve for x:
11) 2(x + 4) = 18
Answer:
x = 5
Step-by-step explanation:
2 (x + 4) = 18
x + 4 = 9
x = 5
Answer:
x=5
Step-by-step explanation:
2(x + 4) = 18
Divide each side by 2
2/2(x + 4) = 18/2
x+4 = 9
Subtract 4 from each side
x+4-4 = 9-4
x=5
Convert 56∘F to ∘C.
Round to one decimal place and do not include units in your answer.
What formula are you using I'm using the one below so hopefully you're able to utilize this.
C = (F-32) ÷ 1.8
C = (56-32) ÷ 1.8
C = ( 24 ) ÷ 1.8
C = 13.3333333
Rounding one decimal place (tenths)
C = 13.3
help Perform the indicated operation.
(-7) · (-5)
-12
-35
12
35
35
Step-by-step explanation:(-7) • (-5)
= 7 • 5
= 7 + 7 + 7 + 7 + 7
= 14 + 7 + 7 + 7
= 21 + 7 + 7
= 28 + 7
= 35
[tex] [/tex]
How many average points per game did Denver score?
The price of a technology stock has risen to $9.66 today. Yesterday's price was $9.53. Find the percentage increase. Round your answer to the nearest tenth of a percent
Answer:
0.13
Step-by-step explanation:
Translate each graph as specified below.
(a) The graph of y=f(x) is shown. Translate it to get the graph of y=f(x) - 4.
(b) The graph of y=g(x) is shown. Translate it to get the graph of y=g(x - 2).
Answer:
1
Step-by-step explanation:
1
The answers are :
a) The graph is translated downwards by 4 units.
b) The graph is translated downwards by 2 units.
What do you mean by translation of a graph ?
The modification of an existing graph or graphed equation to create a different version of the following graph is known as translation.
a)
The graph of y = f(x) is shown.
The other function is y = f(x) - 4.
As it can be observed that the graph is translated from its parent function which is y = f(x) to function y = f(x) - 4.
The graph is shifted down by 4 units or translated downwards by 4 units.
b)
Here , the graph of y = g(x) is shown.
The other function is y = g(x -2)
As we can observe that the graph is translated from its parent function which is y = g(x) to function y = g(x - 2).
The graph is shifted downwards by 2 units or translated downwards by 2 units.
Therefore , the answers are :
a) The graph is translated downwards by 4 units.
b) The graph is translated downwards by 2 units.
Learn more about translation here :
https://brainly.com/question/12861087
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Yep sorry again this math is hard
Answer:
<
Step-by-step explanation:
Firstly, you can focus on the scientific notation and calculate which one is bigger. The left side is [tex]10^3[/tex] whereas the right side is [tex]10^4[/tex]. This shows that even if the number before this was bigger, the larger exponent of these two are the bigger number.
[tex]10^3 = 1000\\10^4 = 10000[/tex]
Meaning the correct sign would be the smaller than sign (<) as the right side is bigger than the left.
Hope this helps!
Graph the function (x) -7x^2
Answer:
See Picture
Step-by-step explanation:
I hope this helps!
Website
1. Orbitz.com
2. Mypoints.com
3. Americangreetings.com
4.Bizrate.com
5.Half.com
Average daily unique visitors
1,527,000
1,356,000
745,000
503,000
397,000
What was the total average number of visits for these websites?
Answer:
905,600 visitors
Step-by-step explanation:
added each number up and divided them by 5 (the total number of websites) to get 905,600