1. Draw the graph of the function,
, using transformations.
Step 1: Check the term x itself,
. It has a power of 1
here. . Then this function is a version of the basic identity function,
.
Step 2: Remember the graph of the basic identity function.
Step 3: Use the following order to graph a function involving more than one
transformation:
. Horizontal translation, f(x+h)
. Stretching or compressing, af(x) or f(bx)
. Reflection, -f(x) or f(-x)
. Vertical translation, f(x) + k
There is no horizontal translation. We have a vertical stretching or
compressing (
Since
, it is a vertical stretch,
(x, 3/2y), replacing each y value with 3/2y (
).
Step 4: We also have a vertical reflection (
) across the x-axis,
replacing each y-coordinate with its opposite (
).
Step 5: Last step is the vertical translation. Vertical translations are quite
intuitive. Graph should be shifted up 3 units here (
).
2. Match the equation with its graph.
With this type of questions, we have to focus on the form of the term. The
first equation has an term in the form of (
). It means
that this equation is a version of the basic identity function ( ), and the
graph of it is:
Only the graph in (b) is similar to this. The second equation represents a
semi-circle with center at the origin and ( ).
Only the graph in (d) is similar to a semi-circle. The third equation has an
term in the form of ( ). It means that this equation is a version
of the squaring function ( ), and the graph of the basic squaring
function is:
Only the graph in (a) is similar to this. The fourth equation has an term in
the form of ( ). It means that this equation is a version of the
basic cubing function ( ), and the graph of it is:
Only the graph in (c) looks like this.
