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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
given f x x2 - 2 x 8 and g x radicx 6 evaluate f 3 and g3solutionokay weve two function evaluations to do here and weve also obtained
coordinates for the point the listed first number is the x-coordinate of the point and the second number listed is the y-coordinate of the point
graphing and functions graphingin this section we have to review some of the fundamental ideas in graphing it is supposed
solve following 3x 2 lt 0solutionnow we know that p ge 0 and thus cant ever be less than
solve following2x - 3 7solutionagain p represents the quantity within the absolute value bars thus all we have to do here is plug into the formula
inequalities involving gt and geonce again lets begin along a simple number
solve following 2 x - 4 10solutionthere actually isnt much to do other than plug into the formula as with equations p merely represents