SOLUTION: Hello, Here is my problematic road block: Consider the function f(x) = (9 - x) / (x + 10) + 2. Algebraically determine the domain and all intercepts. Thank you in advance

Question 905989: Hello,
Here is my problematic road block:
Consider the function f(x) = (9 - x) / (x + 10) + 2. Algebraically determine the domain and all intercepts.
Thank you in advance,
Ryan
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
equation is f(x) = y = (9-x)/(x+10)+2

the domain is undefined when x = -10.

that's because the denominator becomes 0.

the y-intercept is the value of y when x = 0.

when x = 0, the equation becomes f(x) = y = (9-0)/0+10)+2 which becomes f(x) = y = 9/10+2 which becomes f(x) = y = 2.9

the y-intercept is when x = 2.9

the x-intercept occurs when y = 0.

set f(x) = y = 0 = (9-x)/(x+10)+2

shorten this to (9-x)/(x+10)+2 = 0

multiply both sides of the equation by (x+10) to get:

(9-x) + 2(x+10) = 0

simplify to get 9 - x + 2x + 20 = 0

combine like terms to get x + 29 = 0

subtract 29 from both sides of the equation to get x = -29

your x-intercept is x = -29

to summarize, you have:

domain = all real numbers except x = -10
y-intercept equals y = 2.9
x-intercept equals x = -29

a graph of your equation is shown below.

$$$

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