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Sergeeva-Olga [200]
2 years ago
11

If f(x) = x^2 and g(x) = 1/2 f(x + 3) + 6 Describe the transformation(s)​

Mathematics
1 answer:
Bond [772]2 years ago
5 0

Answer:

First, let's define some transformations:

Horizontal translation:

For a function f(x) a horizontal translation of N is written as

g(x) = f(x - N)

If N is positive we have a translation to the right

if N is negative we have a translation to the left.

Vertical translation:

For a function f(x) a vertical translation of N is written as

g(x) = f(x) + N

If N is positive we have a translation up

if N is negative we have a translation down

Vertical dilation.

For a function f(x), a vertical dilation of scale factor k is written as:

g(x) = k*f(x)

Now we can see that in our problem we have:

g(x) = (1/2)*f(x + 3) + 6

Then if we start wit f(x) we have:

first we have a dilation of scale factor k = 1/2

g(x) = (1/2)*f(x)

then we have a translation of 6 units up

g(x) = (1/2)*f(x) + 6

then a translation of 3 units to the left

g(x) = (1/2)*f(x - 3) + 6

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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3 years ago
Please help! Create a set of five positive numbers (repeats allowed) that have a median of 10 and a mean of 14. What thought pro
Brilliant_brown [7]
Alright, since there are 5 numbers, and the mean (or average) is (sum)/(amount of numbers), we have (sum)/5=14. Multiplying both sides by 5, we have the sum being 80. The median of 10 means that in a, b, c, d, e, 10 has to be c and the numbers have to be in ascending order. A and b must be 10 or lower, while d and e must be 10 or higher. Putting some random numbers in, we can have 1, 1, 10, 15, and e. We left e there because the sum needs to be 80, and since 1+1+10+15=27, 80-27=53=e. This, however, would not work if e was less than 10 and we therefore would have needed to make some numbers lower to compensate for this. Our answer is therefore 1, 1, 10, 15, 53
6 0
3 years ago
WILL GIVE BRAINLIEST! Someone please graph these, I can't graph them.
nadezda [96]

Answer:

see attached image

Step-by-step explanation:

F(x) = 2x + 5 is a linear graph because the exponent on x is 1.  I tell my students that think of graphs having one less turn/corner that the value of the highest exponent.  so since 2x has a exponent of 1, 1-1 =0 so it has no turns or its a straight line.

this has a slope of 2 or 2/1 or up 2 and right 1 from the y intercept which is 5

so mark 5 on the y axis and a from there go up 2 and right 1 and make another point.  Join these points and you have your graph


and


g(x) = (x-5)/2  is its inverse and is found:

F(x) = 2x + 5 write it this way y = 2x + 5

now swap the x and y    x = 2y - 5

solve for y

x = 2y + 5

- 5       -5

x - 5 = 2y

/2        /2

(x-5)/2 = y

it can be written as y = x/2 - 5/2

and graphed the same way as above with a  1/2 slope and -5/2 y intercept

4 0
3 years ago
Read 2 more answers
Find the equation of the line that contains the given point and has the given slope-
mylen [45]

Answer:

y-5 = -3x

or

y = -3x+5

Step-by-step explanation:

We can use the point slope form of the equation

y-y1 = m(x-x1)  where m is the slope and (x1,y1) is a point on the line

y-5 = -3(x-0)

y-5 = -3x

We can change it to slope intercept form y= mx+b by adding 5 to each side

y-5+5 = -3x+5

y = -3x+5

3 0
2 years ago
Read 2 more answers
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