Question

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Answer 1

Answer:

$\sqrt{x+6}$

Step-by-step explanation:

So, there are a few things we need to go over to graph a function,

When a number is outside of a root, it changes the y value. For example:

y=$\sqrt{x}+6$

With the +6, y will always be 6 higher than normal.

If it was -6, then y will always be 6 lower than normal.

What if the number is inside the root? Well, it works a little differently.

Instead of changing the y value, it changes the x value. For example:

y=$\sqrt{x+6}$

So if you put a number in for x, lets say -6, wht would you get?

You would get -6+6=0

The square root of 0 is 0, so when x=-6, y=0

Normally, x would have to equal 0 for the y value to be 0.

So basically, when we see the number isnide of the root, we can think the our x coordinate being subtracted by that number.

This makes since, because if we subtract the +6 from x:

x-(+6)= x-6, and -6 is our x coordinate.

If it was -6 at the start, this would also work:

x-(-6)= x+6. So our x coordinate would start at 6.

Now, lets look at our graph.

As we can see, the x values start at -6, and the y values starts at 0.

This eliminates A and D, since the +6 would change the y value, not the x.

Remember that x-6 would make x a postive 6.

x+6 however, would make x a negative 6.

So we need x+6 in a square root.

This eliminates B, since it has a x-6, making the x coordinate postive 6, not negative 6.

So c is our answer.

Hope this helps!