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.