+0

+1
142
2
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The graph of y=f(x) is shown below.

The graph of y=g(x) is shown below.

What is g(x) in terms of f(x)? For example, if you think g(x)=f(x)+1 enter " f(x)+1", without quotation marks.

Thanks, and does use locating points on the graph?

Dec 9, 2018

#1
+100564
+1

Note that the point (2, 0) is on f(x)

And the corresponding point on g(x) is (4, - 4)

So g(x)   is  the graph of  f(x) shifted down 4 units  and vertically " stretched" by a factor of 2

So

g(x) =  f(2x) - 4

Dec 9, 2018
#2
+4221
+1

Close...

We can obtain the graph of $$y=g(x)$$ by taking the graph of $$y=f(x)$$ and stretching it horizontally by a factor of 2, then shifting it down by 4 units. Therefore, $$g(x) = \boxed{f \left( \frac{x}{2} \right) - 4}.$$

Isn't this correct?

tertre  Dec 9, 2018