You may want to go through tutorials on graphing before
starting this tutorial.
Example 1 : Identify the graph of function f(x) = x^{2}  1 Solution to Example 1: The given function f(x) = x^{2}  1 is a
quadratic one and its graph is a parabola. Writing function f in the form f(x) =
a(x  h)^{2} + k makes it easy to graph. The x and y
coordinates of the vertex
are given respectively by h and k. When
coefficient a is positive the parabola opens upward. If a is
negative the parabola opens downward. The given function f can be written as f(x) = (x  0)^{2}
 1. Its vertex has x coordinate equal to 0 and y coordinate equal to 1. Its
coefficient a is negative and the parabola opens downward. Also its y
intercept is at (0 , 1). The above properties of the graph of function f shows that
the graph corresponding to the given equation is graph d.
Example 2 : Identify the graph of function f(x) =
x  1 + 1 Solution to Example 2: The given function f(x) = x  1 + 1 is related to the absolute value function x. We now use a different strategy from the one we used in example 1. The graph of x  1 is the graph of x that has been shifted one unit to the right as shown below. The graph of x  1 + 1 is the graph of x  1 shifted
one unit up as shown below.
The above graph correspond to graph a in
example 2.
Now that you have worked on the above
examples you may go to self test on graphs of functions and solve similar questions.
