I don’t understand it at all and I need it ASAP!

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Step-by-step explanation:

A lot of math is about matching patterns.

For example, ...

  g(x) = f(x -h) +k

means g(x) is the function f(x) translated right by h units and up by k units. This will be true for any expression of f(x).

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In this problem, f(x) = √x. We want to translate it left 6 units (h=-6)*, and up 4 units (k=4).

The notation above means that we will replace x with (x-h) = x+6. and we will add k = 4 to the result.

  f(x) = √x

  g(x) = f(x+6) +4

  g(x) = √(x+6) +4 . . . . . . matches choice D

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* Left is the opposite of right, so left 6 units is the opposite of right 6 units. h=6 for right 6 units, so h=-6 for left 6 units. Then x-h = x-(-6) = x+6.

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Comment on the graph

I find it useful to see a picture with these things. In the attached graphing calculator output, the blue curve is left 6 and up 4 from the red curve. The blue curve is g(x); the red one is f(x).

in problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. to find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

hope it