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this is meant for you to visualize the horizontal asymptote is the horizontal line that the graph approaches as it goes to the right \(\infty\) and to the left \(-\infty\)
they have marked it for you with a dotted line the vertical asymptote is the vertical dotted line. it is hard for me to read, but i think that is the line \(x=-1\)
there are no "oblique asymptotes" otherwise you would see a non vertical line dotted
the domain is all real numbers except where you see that you cannot plug in a value of \(x\) which not coincidentally is the vertical asymptote in other words it is all real numbers except for \(x=-1\)
For domain, how far can x go before being intervened by an asymptote. Same for y. Intercepts, when an x value touches the x-axis or the y value touches the y axis. And you should know asymptotes and what are they. (DOTTED LINES). Give equations and be done with it. Considering this is a test based on what you learned over lessons, I cannot help you further.
and similarly you can see from the graph that the function approaches, but never actually achieves the value of \(y=3\) which is the horizontal asymptote
ohh i see
and finally the "intercepts" are where the graph crosses the \(x\) axis, and where the function crosses the \(y\) axis. it looks like they are at the same place, since the graph crosses both axes at \((0,0)\)
so domain is (-infinity to infinity?
if you have any question let me know. no
all real numbers except -1
domain is all real numbers except \(x=-1\)
and range all real numbers except 3?
i think x-intercept is -1 and y intercept is 3
no the intercept is where it crosses the \(x\) axis, for the \(x\) intercept it is not the same as the asymptotes
it crosses the \(x\) axis at \((0,0)\)
your answer should be an ordered pair \((0,0)\)
well it asks only for the x intercepts
no actually it says "the intercepts" but it is the same answer for both
oh i see well zero for both
ok and vertical is -1 and horizontal?
\(y=3\) is the equation of the dotted horizontal line
i have another problem
post, you will get lots of answers some may even be right