Functions and Graphs - Stage 4
Doesn't Add Up
In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?
Parabolic Patterns
The illustration shows the graphs of fifteen functions. Two of them have equations y=x^2 and y=-(x-4)^2. Find the equations of all the other graphs.
Exploring Cubic Functions
Quadratic graphs are very familiar, but what patterns can you explore with cubics?
Perpendicular Lines
Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?
Negatively Triangular
How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?
Curve Fitter
This problem challenges you to find cubic equations which satisfy different conditions.
At Right Angles
Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?
Tangled Trig Graphs
Can you work out the equations of the trig graphs I used to make my pattern?
Back Fitter
10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?
Surprising Transformations
I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?
What's That Graph?
Can you work out which processes are represented by the graphs?
Functions and Graphs - Short Problems
A collection of short problems on straight line graphs.
Inside a Parabola
A triangle of area 64 square units is drawn inside the parabola $y=k^2-x^2$. Find the value of $k$.
Triangular Slope
Can you find the gradients of the lines that form a triangle?
Graph Triangles
Use the information about the triangles on this graph to find the coordinates of the point where they touch.