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,<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
