Question 254781
Find the domain and the range of these functions.
1. f(x) = 1/sqrt(5+x)
Domain:
The denominator cannot be zero
and 5+x cannot be negative
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Solve 5+x > 0
x > -5
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The domain is "All Real Numbers greater than 5".
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Range:
Since sqrt(5+x)>0, f(x)> 0
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The range is "All Real Numbers greater than 0.
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Graph the equation to see the range:
{{{graph(400,300,-10,10,-10,20,1/sqrt(5+x))}}}
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2. 3y-7x=15
y = (7/3)x + 5
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Its a line with non-zero slope that is not undefined.
Domain and Range are both "All Real Numbers".
{{{graph(400,300,-10,10,-10,10,(7/3)x+5)}}}
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Cheers,
Stan H.