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Natalija [7]
3 years ago
10

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

Mathematics
1 answer:
Ivenika [448]3 years ago
7 0

9514 1404 393

Answer:

  \textbf{D.}\quad g(x)=\sqrt{x+6}+4

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).

__

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

_____

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

__

<em>Comment on the graph</em>

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).

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