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Sketching Curves
Exercise
1.
2.
3.
4.
Sketch the following curves and show their position relative to the curve 𝑦 = 𝑥 3 :
a.
y = (x-2)3
b.
y = (2- x)3
c.
y = (x-1)3
d.
y = (x+2)3
e.
y = -(x+2)3
Sketch the following curves and indicate the coordinates of the points where the curves
cross the axes:
a.
y = (x+3)3
b.
y = (x-3)3
c.
y = (1-x)3
d.
y = -(x-2)3
e.
y = -(x-½ )3
a.
Sketch the curve with equation y = f(x) where f(x) = x2-4.
b.
Sketch the graphs of y = f(4x), y = 3 f(x), y = f(-x) and y = - f(x)
A curve has the equation y = f(x) where f(x) = (x-1)(x-1)(x-6). The points A(0,-6), B(1,0),
C(4,-18) and D(6,0) lie on the curve.
a.
Sketch the curve
b.
Sketch the following graphs and give the coordinates of the points A, B, C and D
after each transformation:
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(i)
f(x+1)
(ii)
f(x)- 4
(iii)
f(2x)
(iv)
3 f(x)
(v)
f( ½ x)
(vi)
½ f(x)
(vii)
f(-x)