Math  /  Algebra

QuestionFind the domain, the x-intercept, and the y-intercept of the function f(x)=52xx+4 f(x) = \frac{5-2x}{x+4} .

Studdy Solution
To find the y-intercept, evaluate f(x) f(x) at x=0 x = 0 :
f(0)=52(0)0+4=54 f(0) = \frac{5 - 2(0)}{0 + 4} = \frac{5}{4}
The y-intercept is (0,54) \left(0, \frac{5}{4}\right) .
The domain of the function is all real numbers except x=4 x = -4 . The x-intercept is (52,0) \left(\frac{5}{2}, 0\right) , and the y-intercept is (0,54) \left(0, \frac{5}{4}\right) .

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