Problema Solution
Determine the x- and y-intercepts of the graph. Write them as points.
Determine the domain and vertical asymptotes, if any, of the function.
Write the domain in interval notation.
Determine the horizontal or oblique asymptote, if any, of the function.
Obtain additional points on the graph. coordinate system and graph the function. Draw the asymptotes using dashed lines. f(x)=x=4/x^2-25
Answer provided by our tutors
to find the x-intercepts set y=0 and solve for x
to find the y-intercepts set x=0 and solve for y
the domain is the possible values of x. find what x cannot be by setting the denominator equal to zero since the denominator cannot equal zero.
interval notation is (_,_) or (_,_] or [_,_) or [_,_] where () means the interval does not include the boundary number and [] means the interval does include the boundary number
the vertical asymptotes occur at the x values when the denominator equals zero
the horizontal asymptote coems from the degrees of the numerator and denominator. if the degree of the numerator is greater than than of the denominator there is no horizontal asymptote, if it is the opposite it is y=0 if they are equal the asymptote is y = the leading coefficients as a fraction
if there is a horzontal asymptote, there is no slant asymptote. to find the slant asymptote you would use long division to solve the polynomial
to find other points on the graph, substitute any values in the domain in for x and solve for y