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:

brainly.com/question/24401156

3 0

1 year ago

A community center is expanding the size

Katen [24]

So the original area is 300*150 (or 45000 ft^2), but now the new area is (300+3y)(150+3y).

The polynomial in standard form would be 45000+900y+450y+9y^2=45000+1350y+9y^2

But the proper way to write it is 9y^2+1350y+45000

When y=4, we get 9(4^2)+1350(4)+45000=9(16)+54000+45000=144+99000=99144

So the new area would be 99144 ft^2

Hope this helped!

6 0

2 years ago

Pls help! Pls do this step by step . factorise: m^3-27

Verdich [7]

Answer:

m-3

Step-by-step explanation:

cube root the two to get m-3

7 0

2 years ago