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### Section 1.10 : Common Graphs

3. Without using a graphing calculator sketch the graph of $$g\left( x \right) = \sin \left( x \right) + 6$$.

Hint : Recall that the graph of $$f\left( x \right) + c$$ is simply the graph of $$f\left( x \right)$$ shifted down by $$c$$ units if $$c < 0$$ or shifted up by $$c$$ units if $$c > 0$$.
Show Solution

Recall the basic Algebraic transformations. If we know the graph of $$f\left( x \right)$$ then the graph of $$f\left( x \right) + c$$ is simply the graph of $$f\left( x \right)$$ shifted down by $$c$$ units if $$c < 0$$ or shifted up by $$c$$ units if $$c > 0$$.

So, in our case if $$f\left( x \right) = \sin \left( x \right)$$ we can see that,

$g\left( x \right) = \sin \left( x \right) + 6 = f\left( x \right) + 6$

and so the graph we’re being asked to sketch is the graph of the sine function shifted up by 6 units.

Here is the graph of $$g\left( x \right) = \sin \left( x \right) + 6$$ and note that to help see the transformation we have also sketched in the graph of $$f\left( x \right) = \sin \left( x \right)$$. 