By using transformations sketch the graph of the given functions.
g ( x ) = x^{2 }+ 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.
g ( x ) = x^{2} + 3
In this case we first have to graph x^{2} (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 x^{2} .
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.