Grace

y=sin(x)
y-coordinates of the minimum= -1
y-coordinates of the maximum = 1
x-intercepts = 0, π, 2 π, 3 π…
TARGETS:
(1) I used CTRL F to find and replace all “x-coordinates” with “x-intercepts” on slide2 (as you
correctly did here below).
(2) Sin(bx) work is very good – I’ve just added that if you had to “describe the transformation of
sin(bx) you’d say a: “horizontal stretch, scale factor = 1/b” (see slide9)
Last slide, coefficient ‘d’, finish off last slide by stating what kind of “transformation” effect “d”
has, is it:
• Rotation (how many degrees & clock or anti-clock?) or Reflection (in what mirror line/axes?)?
• Horizontal or vertical stretch and by what scale factor?
• Horizontal or vertical translation and by what vector?
Superb work Grace
DOUBLE MERIT
- Triple if you finish off the last slide for transformation effect of
Coefficient ‘d’.

y=asin(x)
y=sin(x)
x-intercepts =0, π, 2 π, 3 π…
y=2sin(x)
y=3sin(x)

y=asin(x)
y=sin(x)
y=-2sin(x)
y=-4sin(x)

y=asin(x)
y=sin(x)
y=1.3sin(x)
y-coordinates of the minimum= -1.3
y-coordinates of the maximum = 1.3
y=3.4sin(x)

y=asin(x)
→ When a is positive, the graph is stretched in
the y-axis by the value of a.
→ When a is negative, the graph is flipped in the
x-axis and stretched in the y-axis by the value
of a.
→ When a is a non-integer value, the graph is
stretched in the yaxis by the value of a. If it is
also negative, the graph is flipped in the x-axis.
Very clear explanation and 100%
accurate with negative, decimals
and integers all considered.
Very thorough approach.

y=sin(bx)
y=sin(x)
y=sin(2x)
x-intercepts =0, π/2, π, 3/2π, 4/2π…
y=sin(3x)
x-intercepts =0, 1/3π, 2/3π, π, 4/3π…

y=sin(bx)
y=sin(x)
y=sin(-2x)
x-intercepts =0, π/2, π, 3/2π, 4/2π…
y=sin(-4x)
x-intercepts =0, 1/4π, 2/4π, 3/4π, π…

y=sin(bx)
y=sin(x)
y=1.3sin(x)
x-intercepts =1.3π,
y=3.4sin(x)
x-intercepts =

y=sin(bx)
Whether b is positive, negative or a non-
integer value it makes the coordinates of the
x-intercepts be divided by the value of b.
V.Good – this is a horizontal stretch, scale factor = 1/b

y=sin(x-45)+c
y=sin(x)
y=sin(x-45)

y=sin(x-45)+c
y=sin(x)
y=sin(x-45)
y=sin(x-45)+2
y-coordinates of the minimum= 1

y=sin(x-45)+c
y=sin(x)
y=sin(x-45)-2
y-coordinates of the maximum = -1

y=sin(x-45)+c
y=sin(x)
y=sin(x-45)-2
y=sin(x-45)+2.5
y-coordinates of the minimum= 1.5

y=sin(x-45)+c
Whether c is positive, negative or a non-
integer value, the value of c is the value that
the graph moves up or down by. If the value
of c is positive the graph moves down, if it is
negative the graph moves up.

y=sin(x-d)
y=sin(x-2)
y=sin(x)

y=sin(x-d)
y=sin(x+2)
y=sin(x)

y=sin(x-d)
y=sin(x-1.3)
y=sin(x)

y=cos(x)
x-intercepts = - π /2, π /2, 3π/2, 5π/2…

y=acos(x)
y=cos(x)
x-intercepts =- π /2, π /2, 3π/2, 5π/2…
y=2cos(x)
y=3cos(x)

y=acos(x)
y=cos(x)
y=-2cos(x)
y=-4cos(x)

y=acos(x)
y=sin(x)
y=1.3cos(x)
y=3.4cos(x)
y=cos(x)

y=acos(x)
→ When a is positive, the graph is stretched in
the y-axis by the value of a.
→ When a is negative, the graph is flipped in the
x-axis and stretched in the y-axis by the value
of a.
→ When a is a non-integer value, the graph is
stretched in the yaxis by the value of a. If it is
also negative, the graph is flipped in the x-axis.

y=cos(bx)
y=sin(x)
y=cos(2x)
x-intercepts =0, 1/3π, 2/3π, π, 4/3 π, 5/3 π…
y=cos(3x)
x-intercepts =0, 1/4 π, 2/4 π, 3/4 π, π…
y=cos(x)

y=cos(bx)
y=sin(x)
y=cos(-2x)
x-intercepts =1/3π, 2/3π, 4/3 π, 5/3 π…
y=cos(-4x)
x-intercepts =1/5π, 2/5π, 3/5π, 4/5π, 6/5 π
y=cos(x)

y=COS(bx)
y=sin(x)
y=cos(1.3x)
x-intercepts =
y=cos(3.4x)
x-intercepts =
y=cos(x)

y=cos(bx)
Whether b is positive, negative or a non-
integer value it makes the coordinates of the
x-intercepts be divided by the value of b.

y=cos(x)
y=cos(x-45)+c
y=cos(x-45)

y=cos(x-45)+c
y=cos(x-45)+2
y-coordinates of the minimum= 1
y=cos(x)

y=cos(x-45)+c
y=cos(x-45)-2
y-coordinates of the maximum = -1
y=cos(x)

y=cos(x-45)+c
y=cos(x-45)+1.3
y-coordinates of the minimum= 0.3
y=cos(x)

y=cos(x-45)+c
Whether c is positive, negative or a non-
integer value, the value of c is the value that
the graph moves up or down by. If the value
of c is positive the graph moves down, if it is
negative the graph moves up.

y=cos(x-d)
y=cos(x-2)
y=cos(x)

y=cos(x-d)
y=cos(x+2)
y=cos(x)

y=cos(x-d)
y=cos(x-1.3)
y=cos(x)
Very good work again Grace, so finish it off by stating what kind of “transformation” effect “d” has, is it:
• Rotation (how many degrees & clock or anti-clock?) or Reflection (in what mirror line/axes?)?
• Horizontal or vertical stretch and by what scale factor?
• Horizontal or vertical translation and by what vector?

Grace

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