x2 t07 03 addition, subtraction, multiplication & division (2011)
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(D) Addition & Subtraction of Ordinates
(D) Addition & Subtraction of Ordinates
y = f(x) + g(x) can be graphed by first graphing y = f(x) and y = g(x) separately and then adding their ordinates together.
(D) Addition & Subtraction of Ordinates
y = 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.
(D) Addition & Subtraction of Ordinates
y = 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.
xxy 1 e.g.
(D) Addition & Subtraction of Ordinates
y = 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.
xxy 1 e.g.
xy
xy 1
(D) Addition & Subtraction of Ordinates
y = 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.
xxy 1 e.g.
xy
xy 1
(D) Addition & Subtraction of Ordinates
y = 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.
xxy 1 e.g.
xy
xy 1
xxy 1
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.
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 sin e.g.
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 sin e.g.
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 sin e.g.
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 sin e.g.
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 sin e.g.
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 sin e.g.
(E) Multiplication of FunctionsThe 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.
32 11 e.g. xxxy
32 11 e.g. xxxy
32 11 e.g. xxxy
32 11 e.g. xxxy
32 11 e.g. xxxy
32 11 e.g. xxxy
32 11 e.g. xxxy
32 11 e.g. xxxy
32 11 e.g. xxxy
(F) Division of Functions
by; graphed becan ofgraph Thexgxfy
(F) Division of Functions
by; graphed becan ofgraph Thexgxfy
Step 1: First graph y = f(x) and y = g(x) separately.
12
21 e.g.
xxxxy
12
21 e.g.
xxxxy
(F) Division of Functions
by; graphed becan ofgraph Thexgxfy
Step 1: First graph y = f(x) and y = g(x) separately.Step 2: Mark in vertical asymptotes
12
21 e.g.
xxxxy
(F) Division of Functions
by; graphed becan ofgraph Thexgxfy
Step 1: First graph y = f(x) and y = g(x) separately.Step 2: Mark in vertical asymptotesStep 3: Shade in regions in which the curve must be (same as
multiplication.
12
21 e.g.
xxxxy
12
21 e.g.
xxxxy
12
21 e.g.
xxxxy
12
21 e.g.
xxxxy
12
21 e.g.
xxxxy
12
21 e.g.
xxxxy
12
21 e.g.
xxxxy
(F) Division of Functions
by; graphed becan ofgraph Thexgxfy
Step 1: First graph y = f(x) and y = g(x) separately.Step 2: Mark in vertical asymptotesStep 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)
(F) Division of Functions
by; graphed becan ofgraph Thexgxfy
Step 1: First graph y = f(x) and y = g(x) separately.Step 2: Mark in vertical asymptotesStep 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)
221
22
1221
2
2
2
xxx
xxxx
xxxxy
(F) Division of Functions
by; graphed becan ofgraph Thexgxfy
Step 1: First graph y = f(x) and y = g(x) separately.Step 2: Mark in vertical asymptotesStep 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)
221
22
1221
2
2
2
xxx
xxxx
xxxxy
1:asymptote horizontal y
12
21 e.g.
xxxxy
12
21 e.g.
xxxxy
12
21 e.g.
xxxxy
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