2. (D) Addition & Subtraction of
Ordinatesy = f(x) + g(x) can be graphed by first graphing y = f(x) and y = g(x)
separately and then adding their ordinates together.
3. (D) Addition & Subtraction of
Ordinatesy = f(x) + g(x) can be graphed by first graphing y = f(x) and y = g(x)
separately and then adding their ordinates together.
NOTE: First locate points on y = f(x) + g(x) corresponding to f(x)=0 and
g(x)=0, then plot further points by addition and subtraction of ordinates
and finally locate the position of stationary points.
4. (D) Addition & Subtraction of
Ordinatesy = f(x) + g(x) can be graphed by first graphing y = f(x) and y = g(x)
separately and then adding their ordinates together.
NOTE: First locate points on y = f(x) + g(x) corresponding to f(x)=0 and
g(x)=0, then plot further points by addition and subtraction of ordinates
and finally locate the position of stationary points.
x
xy
1
e.g.
5. (D) Addition & Subtraction of
Ordinatesy = f(x) + g(x) can be graphed by first graphing y = f(x) and y = g(x)
separately and then adding their ordinates together.
y
x
NOTE: First locate points on y = f(x) + g(x) corresponding to f(x)=0 and
g(x)=0, then plot further points by addition and subtraction of ordinates
and finally locate the position of stationary points.
x
xy
1
e.g.
xy
x
y
1
6. (D) Addition & Subtraction of
Ordinatesy = f(x) + g(x) can be graphed by first graphing y = f(x) and y = g(x)
separately and then adding their ordinates together.
y
x
NOTE: First locate points on y = f(x) + g(x) corresponding to f(x)=0 and
g(x)=0, then plot further points by addition and subtraction of ordinates
and finally locate the position of stationary points.
x
xy
1
e.g.
xy
x
y
1
7. (D) Addition & Subtraction of
Ordinatesy = f(x) + g(x) can be graphed by first graphing y = f(x) and y = g(x)
separately and then adding their ordinates together.
y
x
NOTE: First locate points on y = f(x) + g(x) corresponding to f(x)=0 and
g(x)=0, then plot further points by addition and subtraction of ordinates
and finally locate the position of stationary points.
x
xy
1
e.g.
xy
x
y
1
x
xy
1
8. y = f(x) – g(x) can be graphed by first graphing y = f(x) and y = – g(x)
separately and then adding the ordinates together.
9. y = f(x) – g(x) can be graphed by first graphing y = f(x) and y = – g(x)
separately and then adding the ordinates together.
xxy sine.g.
10. y = f(x) – g(x) can be graphed by first graphing y = f(x) and y = – g(x)
separately and then adding the ordinates together.
xxy sine.g.
11. y = f(x) – g(x) can be graphed by first graphing y = f(x) and y = – g(x)
separately and then adding the ordinates together.
xxy sine.g.
12. y = f(x) – g(x) can be graphed by first graphing y = f(x) and y = – g(x)
separately and then adding the ordinates together.
xxy sine.g.
13. y = f(x) – g(x) can be graphed by first graphing y = f(x) and y = – g(x)
separately and then adding the ordinates together.
xxy sine.g.
14. y = f(x) – g(x) can be graphed by first graphing y = f(x) and y = – g(x)
separately and then adding the ordinates together.
xxy sine.g.
15. (E) Multiplication of Functions
The graph of y = f(x). g(x) can be graphed by first graphing y = f(x) and
y= g(x) separately and then examining the sign of the product. Special
note needs to be made of points where f(x) = 0 or 1, or g(x) = 0 or 1.
NOTE: The regions on the number plane through which the graph must
pass should be shaded in as the first step.
29. (F) Division of Functions
by;graphedbecanofgraphThe
xg
xf
y
Step 1: First graph y = f(x) and y = g(x) separately.
Step 2: Mark in vertical asymptotes
31. (F) Division of Functions
by;graphedbecanofgraphThe
xg
xf
y
Step 1: First graph y = f(x) and y = g(x) separately.
Step 2: Mark in vertical asymptotes
Step 3: Shade in regions in which the curve must be (same as
multiplication.
39. (F) Division of Functions
by;graphedbecanofgraphThe
xg
xf
y
Step 1: First graph y = f(x) and y = g(x) separately.
Step 2: Mark in vertical asymptotes
Step 3: Shade in regions in which the curve must be (same as
multiplication.
Step 4: Investigate the behaviour of the function for large values of x
(find horizontal/oblique asymptotes)
40. (F) Division of Functions
by;graphedbecanofgraphThe
xg
xf
y
Step 1: First graph y = f(x) and y = g(x) separately.
Step 2: Mark in vertical asymptotes
Step 3: Shade in regions in which the curve must be (same as
multiplication.
Step 4: Investigate the behaviour of the function for large values of x
(find horizontal/oblique asymptotes)
2
2
1
2
2
12
21
2
2
2
xx
x
xx
xx
xx
xx
y
41. (F) Division of Functions
by;graphedbecanofgraphThe
xg
xf
y
Step 1: First graph y = f(x) and y = g(x) separately.
Step 2: Mark in vertical asymptotes
Step 3: Shade in regions in which the curve must be (same as
multiplication.
Step 4: Investigate the behaviour of the function for large values of x
(find horizontal/oblique asymptotes)
2
2
1
2
2
12
21
2
2
2
xx
x
xx
xx
xx
xx
y
1:asymptotehorizontal y