2. Each of these equations is of the form y = (x-2) + c where c is an integer ranging from -4 to 4. Again the lines are parallel with slope 1. The integer c plays exactly the same role in vertical or horizontal shifting as in problem 1. The set of #2 graphs can be seen as shift of the set of #1 graphs +2 units horizontally, with y = x-2 playing the role of the base graph that y = x played above. Alternately, each of the #2 graphs can be seen as a vertical shift by -2 units from the corresponding #1 graph. (Note that y = (x-2)+c = x + (c-2) = (x+c) -2.)
3. Each of these equations is of the form y = c (x-2) where
c is an integer ranging from -4 to 4. All eight of the lines are concurrent
at the point (2,0). None of the lines are parallel. The value of c determines
the slope of the line. As c ranges from -4 to 0 to 4, the slopes of the
resulting lines range from large negative to 0 to large positive. As a
result, the line behavior ranges from rapidly decreasing from left to right
to remaining constant at y=0 to rapidly increasing from left to right.
Each graph y = c(x-2) represents a rotation of the base graph y=1(x-2)
about the key point (2,0).
4. Each of these equations is of the form y = x^2 + c, where c is
an integer ranging from -3 to 3. The value of c is number of units that
each graph is shifted from the base parabola y=x^2. The result is a set
of nested, non-intersecting parabolas with vertices on the y-axis at (0,c).
5. Each of these equations can be written in the form y =
(x - c)^2. For example y = the c value for (x+3)^2 is -3. The range of
c values is integers from -3 to 3. The value of c represents the number
of units each graph is shifted horizontally from the base graph parabola
y = (x+0)^2. The result is set of overlapping parabolas with vertices on
the x-axis at (c,0).
