range

[smile4me8d21]

What is the range of (x-2)/[(x^2)+(3x)-2]? Is it (-infinity,0) U (0, infinity)?

 

[wjm11]

What is the range of (x-2)/[(x^2)+(3x)-2]? Is it (-infinity,0) U (0, infinity)?

I assume you mean, What is the range of f(x) = (x-2)/[(x^2)+(3x)-2]? Your choice of (-infinity,0) U (0, infinity) makes me suspect that you are considering a horizontal asymptote. Would that be correct?

Consider, however, that when x = 2, f(x) = 0.

A horizontal asymptote is not necessarily a "hard" asymptote like a vertical asymptote. The function may pass through the horizontal asymptote in regions "near" the origin. Horizontal asymptotes describe the "end" behaviors of the function -- the values the function approaches for large positive or negative values of x.

Hope that helps.

 

[smile4me8d21]

Im confused with range then I don't get what it is then

I assume you mean, What is the range of f(x) = (x-2)/[(x^2)+(3x)-2]? Your choice of (-infinity,0) U (0, infinity) makes me suspect that you are considering a horizontal asymptote. Would that be correct?

Consider, however, that when x = 2, f(x) = 0.

A horizontal asymptote is not necessarily a "hard" asymptote like a vertical asymptote. The function may pass through the horizontal asymptote in regions "near" the origin. Horizontal asymptotes describe the "end" behaviors of the function -- the values the function approaches for large positive or negative values of x.

Hope that helps.

 

[wjm11]

http://www.purplemath.com/modules/fcns2.htm