General HSC Mathematics Study Cards
Linear & Non-linear Relarionships - HSC Maths
Linear & Non-linear Relarionships - HSC Maths
1.
2.
Linear functions have an
independent variable with an
index of . . .
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The equation of a
linear function is of the forms . .
.
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y = mx + b
1
or
(e.g. y = 2x + 1)
ax + by + c = 0
Linear & Non-linear Relarionships - HSC Maths
Linear & Non-linear Relarionships - HSC Maths
3.
4.
Linear Functions have a graph
that looks like ...
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Quadratic functions have
an independent variable with
an index of . . .
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2
(e.g. y = x2 + 2x + 1)
A Straight Line
General HSC Mathematics Study Cards
Linear & Non-linear Relarionships - HSC Maths
Linear & Non-linear Relarionships - HSC Maths
5.
6.
The equation of a quadratic
function is of the form ...
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Quadratic Functions have
a graph that looks like ...
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y
y = ax2 + bx + c
(x > 0)
x
A Parabola
(x > 0)
Linear & Non-linear Relarionships - HSC Maths
Linear & Non-linear Relarionships - HSC Maths
7.
8.
If a quadratic equation
(y = ax2 + bx + c) has a>0 then
it is a ...
If a quadratic equation
(y = ax2 + bx + c) has a<0 then
it is a ...
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Minimum
Concave Up
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Maximum
Concave Down
y
x
e.g. y = 2x2 + x + 1
e.g. y = -2x2 + x + 1
General HSC Mathematics Study Cards
Linear & Non-linear Relarionships - HSC Maths
Linear & Non-linear Relarionships - HSC Maths
9.
10.
The equation of a hyperbolic
function is of the forms ...
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Hyperbolic functions have
a graph that looks like ...
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a
x
(x  0)
y
A Hyperbola.
(for x>0)
Linear & Non-linear Relarionships - HSC Maths
Linear & Non-linear Relarionships - HSC Maths
11.
12.
Cubic functions have an
independent variable
with an index of ...
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The equation of a cubic function
is of the forms ...
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3
y = ax3
(e.g. y = 2x3)
(for x > 0)
General HSC Mathematics Study Cards
Linear & Non-linear Relarionships - HSC Maths
Linear & Non-linear Relarionships - HSC Maths
13.
14.
Cubic functions have a graph
that looks like ...
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Exponential functions have an
independent variable with an
index of ...
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X
y
(e.g. y = 2x)
x
A Cubic
(for x>0)
Linear & Non-linear Relarionships - HSC Maths
Linear & Non-linear Relarionships - HSC Maths
15.
16.
The equation of a exponential
function is of the forms ...
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Exponential functions have a
graph that looks like ...
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y = b (ax)
(x > 0)
An exponential curve.
(for x>0)
General HSC Mathematics Study Cards
Linear & Non-linear Relarionships - HSC Maths
Linear & Non-linear Relarionships - HSC Maths
17.
18.
If a exponential equation
[y = b (ax3)] has a>1 then it
is . . .
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If a exponential equation
[y = b (ax3)] has 0<a<1 then it
is . . .
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Growing
Decaying
Linear & Non-linear Relarionships - HSC Maths
Linear & Non-linear Relarionships - HSC Maths
19.
20.
Direct Variation means that . . . Inverse Variation means that . . .
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As one variable increases, the
other variable increases.
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As one variable increases, the
other variable decreases.
General HSC Mathematics Study Cards
Linear & Non-linear Relarionships - HSC Maths
Linear & Non-linear Relarionships - HSC Maths
21.
22.
Direct Variation
Inverse Variation
y varies directly with x
is written as . . .
y varies inversely with x
is written as . . .
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y x
y  kx
1
y
x
k
y
x
Linear & Non-linear Relarionships - HSC Maths
Linear & Non-linear Relarionships - HSC Maths
23.
24.
Direct Variation
Example.
Inverse Variation
Example.
y varies directly with x.
y = 6 when x = 2
y varies inversely with x.
y = 6 when x = 2
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y x
y  kx
6  k2
k 3
i.e. y  3x
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k
y
x
k
y
x
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k
2
k  12
12
i.e. y 
x
6