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By using transformations sketch the graph of the given functions.
g ( x ) = x2 + 3
Solution
Here the first thing to do is graph the function without the constant which by this point must be quite simple for you. Then shift accordingly.
In this case we first have to graph x2 (the dotted line on the graph below) & then pick this up & shift it upwards through 3. Coordinate wise it will mean adding 3 onto all the y coordinates of points on x2 .
Following is the sketch for this one.
Hence, vertical shifts aren't all that bad if we are able to graph the "base" function first. Note as well which if you're not sure that you believe the graphs in the earlier set of examples all you have to do is plug a couple values of x into the function & check that they are in fact the correct graphs.
It is probably the easiest function which we'll ever graph and still it is one of the functions which tend to cause problems for students. The most general form for the constant
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Let's begin with the graph of couple of polynomials. Do not worry regarding the equations for these polynomials. We are giving these just so we can utilize them to show so
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