What happens when a constant like "2" is added or subtracted to all of a rational function? Is it the same as what happens when it is added/subtracted to a quadratic function in standard form?
Basically, yes. However, if you'd like to use all the ideas we've developed about the numerator and denominator of rational functions, you might be better off getting a common denominator and combining the fractions.
I'm super confused about using asymptotes to write an equation. Sometimes i understand what is going on and other times i get knocked down by confusion. Help!
It's just the horizontal asymptote that can be crossed. The graph of a function will never intersect its vertical asymptotes. The horizontal asymptotes are related to end behavior, so really only come into play when the value of x is very large. As such, when the value of x is relatively small (i.e., the middle of the graph), the horizontal asymptote is irrelevant.
The only exceptions are when there is a zero of multiplicity two in the denominator. When that happens, the graph will go the same direction on both sides of the vertical asymptote that came from the repeated factor.
I dont understand how to get the answer of a complex number that is in fraction form. For example, (2-2i)/(3+4i). I just don't know how to go about solving a problem like that.
How to determine when you will have imaginary solutions on a graph.
ReplyDeleteDetermining the domain of a function in the classic "write ... as a function of x" problems.
ReplyDelete-Adam Peirce
How to figure out the notation of a function by looking at a graph
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ReplyDeleteWhat happens when a constant like "2" is added or subtracted to all of a rational function? Is it the same as what happens when it is added/subtracted to a quadratic function in standard form?
ReplyDeleteBasically, yes. However, if you'd like to use all the ideas we've developed about the numerator and denominator of rational functions, you might be better off getting a common denominator and combining the fractions.
DeleteHow do you write an equation for a rational function when given the asymptotes and if it passes through a certain point?
ReplyDeleteHow would one determine where (if any) imaginary solutions are placed in a graph?
ReplyDeleteI'm super confused about using asymptotes to write an equation. Sometimes i understand what is going on and other times i get knocked down by confusion. Help!
ReplyDeleteHow can graphs have asymptotes and then cross them? They do but I don't understand why.
ReplyDeleteIt's just the horizontal asymptote that can be crossed. The graph of a function will never intersect its vertical asymptotes. The horizontal asymptotes are related to end behavior, so really only come into play when the value of x is very large. As such, when the value of x is relatively small (i.e., the middle of the graph), the horizontal asymptote is irrelevant.
DeleteDo graphs ever cross the horizontal and vertical asymptotes or is that not possible?
ReplyDeleteSee my reply to Julia's post, just above yours.
DeleteWhat happens when the 90% truth about having the graphs doing the opposite actions with each other inst true. What would be an example of an equation?
ReplyDeleteThe only exceptions are when there is a zero of multiplicity two in the denominator. When that happens, the graph will go the same direction on both sides of the vertical asymptote that came from the repeated factor.
DeleteWhen looking at a graph, how can you determine the number of imaginary zeros at a given point?
ReplyDeleteI can't understand very well the end behavior and the reason why a graph can intersect horizontal asymptotes and not vertical ones.
ReplyDeleteWhat changes the horizontal asymptote?
ReplyDeleteI dont understand how to get the answer of a complex number that is in fraction form. For example, (2-2i)/(3+4i). I just don't know how to go about solving a problem like that.
ReplyDeletehow do you find the slant asymptote of an equation?
ReplyDelete