sakigirl
How do you find the domain and range of y=(1/x)-5?
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sakigirl
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I already graphed.
sakigirl
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|dw:1359707995799:dw|
dpaInc
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notice the vertical asymptote... at x = ???
this should give you a hint for the domain...
notice the horizontal asymptote... at y = ???
this should give you a hint for the range.
skullpatrol
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What happens at x = 0?
jim_thompson5910
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Hint: To find the domain, find all the values of x that make the denominator equal to zero
To find the range, find the inverse function and repeat the same steps to find the domain
sakigirl
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I'm confused with this one because there are two lines. It throws me off. Should I put them together or what?
skullpatrol
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What do the "lines" mean?
sakigirl
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I'm not really sure what they mean, they're just lines
sakigirl
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The two curve lines
skullpatrol
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|dw:1359708410347:dw|
skullpatrol
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What is the domain and range of this equation?
sakigirl
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This is what I'm having trouble with. I don't know how to find the domain and the range for these kinds of functions
skullpatrol
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The domain is all the values that you are allowed to input into the equation.
jim_thompson5910
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ignore the graph
look at the equation y = (1/x) - 5
x cannot be 0 because if it were, then you would be dividing by zero (which is not allowed)
so you must restrict 0 from the domain
any other number is just fine
So the domain is the set of all real numbers but x cannot be zero
jim_thompson5910
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the range can be found in a similar way, but you first need to find the inverse function
skullpatrol
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What would those be for $$y=\frac{1}{x}$$
sakigirl
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What do you do after you find the inverse function?
jim_thompson5910
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what did you get for the inverse function
sakigirl
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Actually, nevermind.
sakigirl
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I want to be able to look at the graph and know the domain and the range
jim_thompson5910
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I'll show you how to get the inverse function
Swap x and y, then solve for y
y = (1/x) - 5
x = (1/y) - 5
x+5 = 1/y
y(x+5) = 1
y = 1/(x+5)
So the inverse function is y = 1/(x+5)
jim_thompson5910
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what makes the denominator x+5 equal to zero ?
jim_thompson5910
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we can go back to the graph after we do these equations
sakigirl
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Wait, hold on. @skullpatrol is it |dw:1359709153164:dw|
skullpatrol
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Yes, and why?
skullpatrol
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|dw:1359709317420:dw|
skullpatrol
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|dw:1359709670237:dw|
skullpatrol
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Compare your graph to mine :)
sakigirl
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That's what I got
sakigirl
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x=/=0
y=/=-5