Part 1:
1.
(a)
(i). f(x) +2 = 3x + 2
(ii). f(x) -3 = 3x - 3
(iii). f(x) +6 = 3x + 6
(b)
2.
(a)
(i). f(x) +2 = x3 + 2
(ii). f(x) -3 = x3 - 3
(iii). f(x) +6 = x3 + 6
(b)
3.
To comprehend this transformation, imagine a graph that shows the relationship between the values of
y and x as defined by the function y=f(x). This function is a collection of (x,y) pairs that satisfy the
equation y=f(x), and the graph is a visual representation of these pairs on a coordinate plane.
By adding a constant value d to the function, we move the entire graph upward by d units. This means
that for every (x,y) pair in the original graph, we now have a corresponding pair (x,y+d) in the new
graph.
This transformation can be expressed mathematically as follows:
y=f(x) --> y=f(x)+d
Here, y=f(x) denotes the original function, while y=f(x)+d denotes the transformed function. The
transformation is essentially a vertical shift of the function by d units.
Part 2:
1.
(a)
(i). 3x + 6 = 3f(x)
(ii). x/2 + 1 = ½f(x)
(iii). 5x+10 = 5f(x)
B.
C.
The transformation y=pf(x) multiplies the distance of each point from the x-axis by a positive constant
p.
D.
Its possible for a point on the graph of y=f(x) to not move under the transformation y=pf(x) if the
value of f(x) is zero at that point. These points are called x-intercepts of the graph.
2.
(a)
(i). 2x+2 = f(2x)
(ii). x/3 + 2 = f(1/3x)
(iii). 4x+2 = f(4x)
B..
C.
The transformation y=f(qx) multiplies the distance of each point from the y-axis by a positive constant
q.
D.
Yes, it is possible for a point on the graph of y=f(x) to not move under the transformation y=f(qx) if
the value of f(x) is zero at that point. These points are called y-intercepts of the graph.
1.
(a)
(i). -2x-3= -f(x)
(ii) -2x+3= f(-x)
(b)
2.
(a)
(i) -x3-1 = -f(x)
(ii) -x3+1 = f(-x)
(b)
3.
(a)
The transformation that maps y=f(x) to y=-f(x) is a reflection about the x-axis, which flips the graph
upside down.
(b)
The transformation that maps y=f(x) to y=f(-x) is a reflection about the y-axis, which produces a
graph that is symmetric to the original graph with respect to the y-axis.