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# Multiply ranges

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Suppose that $$f(x)$$ and $$g(x)$$ are functions on $$\mathbb{R}$$ such that the range of $$f$$ is $$[-5, 3]$$, and the range of $$g$$ is $$[-2, 1]$$. The range of $$f(x) \cdot g(x)$$ is $$[a, b]$$. What is the largest possible value of $$b$$?

Aug 18, 2020

#1
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I think this has been answered before...though I do not kow if I was correct.....this one is hard to read....

I believe the range could go as positive as   -5 x -2 = 10

and as negative as -2 x 3 = -6

so  [-6,10]      Let me know if this is correct...or incorrect       (b would be '10' )

Aug 18, 2020
#2
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Thank you a lot! I solved it actually a little while ago, and that answer is right!

Williamjwu8  Aug 19, 2020
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You sound surprised.

Melody  Aug 19, 2020