Please note that this topic is now assessed at NCEA, Level 2 (Year 12).
There are several other types of graphs. These include hyperbolas, circles, growth curves and cubics.
These are shown below.
Hyperbolas
The general equation of a hyperbola is xy = c or
If c is positive. e.g. xy = 4 |
If c is negative. e.g. xy = - 4 |
Circles
The general equation of a circle is x^{ 2} + y^{ 2} = a^{ 2}. , where a is the radius of the circle.
This relation is not a function, because some of the x-values have two corresponding y-values.
e.g. x ^{2} + y ^{2} = 9
Exponential Functions or Growth Curves
The general equation is y = a^{x}
The greater the value of a, the steeper is the curve.
All growth curves of this type pass through the point (0, 1)
e.g. y = 3^{x }
Cubics
The general equation of a cubic function is y = (x − a)(x − b)(x − c)
The simplest cubic is y = x^{3}.
e.g.
y = x^{3} |
y = (x − 1)(x − 3)(x + 2) |
Summary of Graphs
Straight line |
ax + by + c = 0 y = mx + c |
x and y terms both have exponents of 1 |
x + 2y = 6 y = 3x + 4 |
Parabola |
y = ax^{ 2 }+ bx + c y = a(x − h)^{2} + k |
y term has exponent of 1 x term has exponent of 2 |
y = x^{ 2} + 4x + 3 y = 2(x − 3)^{2} + 4 |
Hyperbola |
xy = c |
x and y terms have exponents of 1 |
xy = 6 |
Circle |
x^{ 2} + y^{ 2} = a^{2} |
x and y terms both have exponents of 2 |
x^{ 2 }+ y^{ 2 }= 16 |
Growth curve |
y = a ^{x} |
x is the exponent |
y = 5^{x} |
Cubic |
y = (x − a)(x − b)(x − c) |
x term has exponent of 3 |
y = (x − a)(x − b)(x − c) |