for this rational function f(x)=x^2-3x-10/x^2-1 determine were possible.

Question

1. for this rational function f(x)=x^2-3x-10/x^2-1 determine were possible.

 

i.the domain of the function.

 

ii. the coordinates of the x and y- intercept of the graph of function.

 

iii. vertical asymptote, horizontal asymptote and oblique asymptote of the graph of function.

 

iv. is the function a one-one function? Explain

 

v. is the function an even or odd function? explain

 

vi. Use the graph to solve the inequalities f(x) less than equal to 0,f(x)>0 and f(x)greater than equal to 0.

 

vii. find the domain of g and h, given that g(x)=square root of f(x) and h(x)=log f(x) 

Answer 1

f(x) = (x-5)(x+2)/(x-1)(x+1)

domain is all reals except x=1 or -1

y intercept = -10/-1 = 10 = (0,10)

x intercepts are x=5 or -2 the points (5,0), (-2,0)

vertical asymptotes are x=1 and x=-1

horizontal asymptote is y=1

not one to one. it fails the horizontal line test

it's not odd or even, almost symmetrical about the y axis though, "almost" even