Curve Sketching

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Curve Sketching

• Learning Outcomes
• Make tables and draw the graphs of various
  equations to include Linear Functions
• Quadratic Functions
• Cubic Functions
• Exponential Functions
• Reciprocal Functions
• Trig Functions

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• Match the correct equations with the correct
  graph
• Solve equations graphically
• Interpret the effect of transformation on
  functions to include
• yf(xa) applied to f(x)
• yf(ax) applied to f(x)
• yf(x)a applied to f(x)
• yaf(x) applied to f(x)

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Curve Sketching
Linear Graphs
Linear means y mx c where m
gradient c intercept (y axis) NB
coefficient of y must be 1
(2, 0)
(-0.5, 0)
(-2/3, 0)
(0, -2)
y 3x 2
y -4x 2
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Curve Sketching
Trig Graphs
y sin x
y cos x
y tan x
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Curve Sketching
Quadratic and Cubic Graphs
Quadratic y ax2 bx c
General shape for a 0
General shape for a 0
Cubic y ax3 bx2 cx d
General shape for a 0
General shape for a 0
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Curve Sketching
Reciprocal and Exponential Graphs
Exponential curves y 2x(ax)
Reciprocal curves y 1/x
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Curve Sketching
Curve transformations
Translate along x axis using y x2

• Draw y (x 1)2
• - translation 1 to the left

• Draw y (x - 1)2
• - translation 1 to the right

Translate along y axis using y x2

• Draw y x2 1
• - translation 1 upwards

• Draw y x2 - 1
• - translation 1 downwards

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Curve Sketching
Curve transformations
Stretch along y axis using y sin x

1. Draw y sin 2x

1. Draw y sin x/2

sin x
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Curve Sketching
Curve transformations
y f(x) ? y af(x)
Stretch along y axis

1. Draw y cosx

1. Draw y 2cos x

1. Draw y 2x2

1. Draw y ½x2

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Curve Sketching
Summary
Type Notation Example Effect
Translation
i) Along x axis y F(x a) y sin (x 90) Sine wave moves 90 to the left
ii) Along y axis y F(x) a y x3 -1 x3 moves 1 unit down OY
Stretch
i) Along x axis y F(ax) y sin 2x Compression To make 2 sine waves
ii) Along y axis y aF(x) y 3cos x Stretch scale factor 3
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Curve Sketching
Additional Notes
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Curve Sketching
Learning Outcomes At the end of the topic I will
be able to
Can Revise Do Further

• Make tables and draw the graphs of various
  equations to include Linear Functions
• Quadratic Functions
• Cubic Functions
• Exponential Functions
• Reciprocal Functions
• Trig Functions

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• Match the correct equations with the correct
  graph
• Solve equations graphically
• Interpret the effect of transformation on
  functions to include
• yf(xa) applied to f(x)
• yf(ax) applied to f(x)
• yf(x)a applied to f(x)
• yaf(x) applied to f(x)

?
?
?
?
?
?
?
?
?
?
?
?