5H - Determining the rule of a graph
If we are given the right information it is possible to determine the rule of a graph. Determining the rule of a graph involves:
- Deciding what general equation is appropriate.
- Substituting known information into the general equation.
- Solving for the unknown parameters present in the general equation (often simultaneously).
- Stating the final equation for the function/graph.
5H - Example 2: Determining the rule of a function
A hyperbola with a general equation \(y=\frac{a}{x-h}+k\) is known to have asymptotes at \(x=-4\) and \(y=-2\). The graph also passes through the point \((-3,-4)\). Determine the equation that describes this graph.
|
5H - Example 2: Video solution
5H - Example 2: Practice
Question 1: ABC Question 2: ABC 5H - Example 2: Solutions
Question 1: ABC Question 2: ABC |
5H - Example 3: Determining the rule of a function
A truncus graph has a domain of \(x\in (-\infty,2) \cup (2,\infty)\) and a range of \(y\in (5,\infty)\). The graph also passes through the point \((1,9)\). Determine the equation that describes this graph.
|
5H - Example 3: Video solution
5H - Example 3: Practice
Question 1: ABC Question 2: ABC 5H - Example 3: Solutions
Question 1: ABC Question 2: ABC |
5H - Example 4: Determining the rule of a function (CAS)
A square root graph is known to have an equation \(y=\sqrt{n(x-h)}+k\). If the graph passes through the points \((2,4)\), \((5,3)\) and \((6,2)\), determine the equation that describes this graph.
|
5H - Example 4: Video solution
5H - Example 4: Practice
Question 1: ABC Question 2: ABC 5H - Example 4: Solutions
Question 1: ABC Question 2: ABC |