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kotegsom [21]
2 years ago
5

Give an equation for the result of shifting the graph of up by 4 units, and left by 2 units.

Mathematics
1 answer:
andreyandreev [35.5K]2 years ago
3 0

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

----------------------------------

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,<em> the translation is to the left.</em>

If N is negative, <em>the translation is to the right.</em>

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,<em> the translation is upwards.</em>

If N is negative, <em>the translation is downwards.</em>

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.

<em>The shift up of 4 units is written as:</em>

<em>g(x) = f(x) + 4</em>

<em>The shift of 2 units to the left is written as:</em>

<em>g(x) = f(x + 2) </em>

<em>These two together give:</em>

<em>g(x) =  f(x + 2) + 4.</em>

This is the equation we wanted to get.

If you want to learn more, you can read:

brainly.com/question/24401156

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