h(x) = a/x-p +q. A is the x-intercept and B is the y-intercept

Question

1) If the coordinates of B is (0;-3) determine the values of a, p and q. 2) Determine the coordinates of A 3) Vertical asymptote is (3;0) and horizontal asymptote is (0;-1).Write down the equation of the asymptotes of h. Note: A cuts through the x-axis

Answer 1

Please use paranthesis next time.

Assuming h(x) = a/(x-p)  + q

Given,

i) (0,-3) is a point on the curve.

ii) (3,0) is a vertical asymptote

iii) (0,-1) is a horizontal asymptote

We know that a vertical asymptote occurs when denominator = 0

so at x - p = 0 vertical asymptote will occur.

=> 3 - p = 0

=> p = 3

Since in our function, degree of N(x) < D(x)  (where N(x) is numerator and D(x) is denominator)

Therefore, the horizontal asymptote should occur at x = 0, but the whole function is shifted down by 1 unit (using ii)

So, q = -1

Now using (i) and values of p and q we can find a,

-3 = a/(0-3) - 1

=> -2 = -a/3

=> a = 6

Graph of the function:

Comments

Here is the graph of the function with asymptotes.