How do the graphs of $f (x) = \sqrt{x} + 2$ $f(x)=sqrtx+2$ and $g (x) = \sqrt{x + 2}$ $g(x)=sqrt(x+2)$ compare?

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How do the graphs of $f (x) = \sqrt{x} + 2$ $f(x)=sqrtx+2$ and $g (x) = \sqrt{x + 2}$ $g(x)=sqrt(x+2)$ compare?

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Answer 1 · 2018-01-22T14:03:35

See below.

Explanation:

graph{sqrt(x)-2 [-10, 10, -5, 5]}

For $\sqrt{x} - 2$ $sqrt(x)-2$ , above.

graph{sqrt(x-2) [-10, 10, -5, 5]}

For $\sqrt{x - 2}$ $sqrt(x-2)$ , above.

They are pretty similar, for one fact: doing $f (x) - k$ $f(x)-k$ shifts the graph $k$ $k$ units down, and $f (x) + k$ $f(x)+k$ shifts it $k$ $k$ units up.

On the other hand, doing $f (x - k)$ $f(x-k)$ shifts the graph $k$ $k$ units right, and $f (x + k)$ $f(x+k)$ shifts it $k$ $k$ units left.

And so, the above.

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How do the graphs of $f (x) = \sqrt{x} + 2$ $f(x)=sqrtx+2$ and $g (x) = \sqrt{x + 2}$ $g(x)=sqrt(x+2)$ compare?

1 Answer

Explanation:

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How do the graphs of f(x)=√x+2f(x)=sqrtx+2 and g(x)=√x+2g(x)=sqrt(x+2) compare?

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How do the graphs of $f (x) = \sqrt{x} + 2$ $f(x)=sqrtx+2$ and $g (x) = \sqrt{x + 2}$ $g(x)=sqrt(x+2)$ compare?