SOLUTION: Consider the function f(x)= 4-x/(divided by) x+5 +. Algebraically determine the domain and all intercepts.

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Question 841947: Consider the function f(x)= 4-x/(divided by) x+5 +. Algebraically determine the domain and all intercepts.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Assuming the denominator is x+5, this means that x+5 = 0 ---> x = -5 makes the denominator zero. We CANNOT divide by zero. So x can be any number you want but x cannot be equal to -5

Domain: Set of all real numbers but x%3C%3E-5

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To find the y-intercept, plug in x = 0 and evaluate

y+=+%284-x%29%2F%28x%2B5%29

y+=+%284-0%29%2F%280%2B5%29

y+=+4%2F5

y+=+0.8

The y-intercept is (0, 0.8) or (0, 4/5)

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To find the x-intercept, plug in y = 0 and solve for x

y+=+%284-x%29%2F%28x%2B5%29

0+=+%284-x%29%2F%28x%2B5%29

0%28x%2B5%29+=+4-x

0+=+4-x

x+=+4

The x-intercept is (4,0)