range of graph (1 Viewer)

[waltssillyhat]

would the range of this graph still be (-∞,∞) even though there is an asymptote at y=3? ( i thought otherwise, but this is what it says in the solutions)

 

[coolcat6778]

no

 

[queetle]

range is (- ∞ , 3) and (3, ∞ ), this accounts for the asymptote at y=3

 

[waltssillyhat]

range is (- ∞ , 3) and (3, ∞ ), this accounts for the asymptote at y=3

that's what i thought, but the answers say that the range is (-∞,∞), so i wasn't sure

 

[Water283]

Am I missing something? y=3 looks very achievable on the left side of the graph? The range would be (-∞,∞) in that case.

 

[waltssillyhat]

Am I missing something? y=3 looks very achievable on the left side of the graph? The range would be (-∞,∞) in that case.

i think that there are some cases where a graph can pass through a horizontal asymptote, but they can never cross a vertical asymptote

 

[Socialism]

i can't remember doing a question like that in class so i'm definitely keen to know the solution

 

[cheesynooby]

yes




(range is all the possible y values that a function can output, and at roughly x = -0.5 the y value is 3)
(also generally functions cannot cross a vertical asymptote, but graphs in general can given they aren't a function)

 

[Socialism]

graphs in general can given they aren't a function

????? it passes the vertical line test, doesn't it?
like what do you mean lol... do you mean graphs aren't always a function (got that bit) but wdym the graph that isn't a function cuz like

 

[Study to success]

I’m confused cause why is the graph going through the y=3 asymptote

 

[Socialism]

my question would probably be more coherent if it was a series of question marks with no words tbh

????? it passes the vertical line test, doesn't it?
like what do you mean lol... do you mean graphs aren't always a function (got that bit) but wdym the graph that isn't a function cuz like

 

[funnytomato]

A function would have its function value approaching but never equal the horizontal asymptote value when x approaches infinity/-ve infinity.

But it does NOT mean the function can never takes the value of the horizontal asymptote when x is not approaching infinity/-ve infinity
e.g. f(x) = x/(1+x^2) has horizontal asymptote of y=0 but at x=0 y=0

 

[Water283]

What do you reckon?

 

[coolcat6778]

would the range of this graph still be (-∞,∞) even though there is an asymptote at y=3? ( i thought otherwise, but this is what it says in the solutions)
View attachment 48186

actually its all y, so solutions are correct