Mathematics
Grade10
Easy

Question

What are the equations of the asymptotes of the function?
f(x) = fraction numerator 1 over denominator left parenthesis straight x space plus space 5 right parenthesis end fraction – 3

  1. x = 5 and y = 3
  2. x = -5 and y = -3 
  3. x = 3 and y = -5
  4. x = -3 and y = 5

Hint:

In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity. In projective geometry and related contexts, an asymptote of a curve is a line which is tangent to the curve at a point at infinity.

The correct answer is: x = -5 and y = -3


    We have to find the equation of the asymptotes.
    For the function, f(x) = fraction numerator straight a over denominator left parenthesis straight x space minus space straight h right parenthesis end fraction + k
    Horizontal asymptote: y = k
    Vertical asymptote: x = h
    In this case, asymptotes are x = -5 and y = -3.
    So, the asymptotes to the graph f(x) = 1/(x+5) - 3 are x = -5 and y = -3.
    Hence, the correct option is A.

    The vertical asymptote is y= k and the horizontal asymptote is x=h, where (h,k) is a moving point on the graph.

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