Mathematics
Grade10
Easy
Question
What are the equations of the asymptotes of the function?
f(x) = 
– 3
- x = 5 and y = 3
- x = -5 and y = -3
- x = 3 and y = -5
- 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) = 
+ 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.
