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miscellaneous functionsthe importance of this section is to introduce you with some other functions that dont really need the work to graph that the
there are also two lines on each of the graph these lines are called asymptotes and as the graphs illustrates as we make x large in both the ve and
note that the right side has to be a 1 to be in standard form the point h k is called the center of the ellipseto graph the ellipse all that we
convert following into the convert following into the
as a last topic in this section we have to briefly talk about how to take a parabola in the general form amp convert it into the following
as noted earlier most parabolas are not given in that form so we have to take a look at how to graph a parabola which is in the general
lets go through first form of the parabola f x a x - h 2 kthere
there are two forms of the parabola which we will be looking at the first form will make graphing parabolas very simple unluckily most parabolas
now lets get back to parabolas there is a basic procedure we can always use to get a pretty good sketch of a parabola following it is 1 determine
we have to probably do a quick review of intercepts before going much beyond intercepts are the points on which the graph will cross the x or
the dashed line along with each of these parabolas is called the axis of symmetry every parabola contains an axis of symmetry and as the graph
all parabolas are vaguely u shaped amp they will contain a highest or lowest point which is called the vertex parabolas might open up or down and
given f x 3x - 2 find f -1 x solutionnow already we know what the inverse to this function is as already weve done some work with it though
the process for finding the inverse of a function is a quite simple one although there are a couple of steps which can on occasion be somewhat
here are two one-to-one functions f x and g x if f o g x x
a function is called one-to-one if no two values of x produce the same y it is a fairly simple definition of one-to-one although it takes an instance
in previous section we looked at the two functions f x 3x - 2 and g x x3 23 and saw
given fx 23x-x2 and gx 2x-1 evaluate fg x fogx and gof xsolutionthese are the similar functions that we utilized in the first set of
we have to note a couple of things here regarding function composition primary it is not multiplication regardless of what the notation may
now we need to discuss the new method of combining functions the new way of combining functions is called function composition following is the
given f x 2 3x - x2 and g x 2 x -1 evaluate f g 4solutionthrough evaluate we mean one of two things based on what is in the
the topic along with functions which we ought to deal with is combining functions for the most part this means performing fundamental arithmetic
now we need to discuss graphing functions if we recall from the earlier section we said thatf x is nothing more than a fancy way of writing y it
find out the domain of each of the following functionsg x x3 x2 3x -10solutionthe domain for this function is all of the values of x for which we
domain and rangethe domain of any equation is the set of all xs which we can plug in the equation amp get back a real number for y the range of any