Which of the following transforms y=x2 to the graph of y=(x+5)2? a translation 5 units to the right a translation 5 units to the left a translation 5 units down a translation 5 units up

We define transformations as operations that act on functions and modify them in some way. Here we will see translations, which is a type of transformation that moves the whole graph in some direction.

We will see that this is a translation of 5 units to the left.

To solve this, first, we need to describe what a horizontal translation is.

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

g(x) = f(x + N).

So here we start wit:

f(x) = x^2

And then we have:

g(x) = (x + 5)^2

Then we can see that:

g(x) = f(x + 5).

From this, we can conclude that N = 5, thus we have a translation of 5 units to the left.

If you want to learn more, you can read:

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Translation 5 units to the left

The "x+5" replaces the "x", meaning that the xy axis moves 5 units to the right. If the parabola stays still, then a point like (0,0) moves to (-5,0) after you move the xy axis 5 units to the right. If the xy axis stays still, then it gives the illusion that the entire parabola moves 5 units to the left.

Check out the graph below for the comparison of the two graphs. Note that the blue graph moves 5 units to the left to get the red graph. In other words, every point on the blue graph moves 5 units to the left to get a corresponding point on the red graph.