Question

For each function,
i) determine the corresponding reciprocal
function, y =1/f(x)

ii) state the non-permissible values of
x and the equation(s) of the vertical
asymptote(s) of the reciprocal function
iii) determine the x-intercepts and the
y-intercept of the reciprocal function
iv) sketch the graphs of y = f(x) and
y = 1/f(x) on the same set of axes
a) f(x) = x^2 - 25
b) f(x) = x^2 - 6x + 5

Answer 1

I will do the first, you do the second

f(x) = x^2 - 25
let g(x) = 1/(x^2 - 25)

graphs: I assume you know what the parabola looks like, here is the reciprocal
http://www.wolframalpha.com/input/?i=plot++y+%3D+1%2F%28x%5E2+-+25%29

notice that at the x-intercepts of the first one, namely x=±5, the reciprocal has asymptotes,
so vertical asymptotes at x = ± 5

there are no x-intercepts, (since 1/(x^-25) can never be zero.
for the y-intercept , let x = 0
so 1/(0-25) = -.04 (see graph)

Answer 2

Thank you so much, the second one is easy now :)