There are 49 NRICH Mathematical resources connected to Graph sketching, you may find related items under Coordinates, functions and graphs.
Broad Topics > Coordinates, functions and graphs > Graph sketching
Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?
Can you work out which processes are represented by the graphs?
Can you sketch graphs to show how the height of water changes in different containers as they are filled?
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?
Can you work out the equations of the trig graphs I used to make my pattern?
Various solids are lowered into a beaker of water. How does the water level rise in each case?
This problem challenges you to find cubic equations which satisfy different conditions.
Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?
How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?
Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.
Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.
Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.
Use the interactivity to move Pat. Can you reproduce the graphs and tell their story?
The family of graphs of x^n + y^n =1 (for even n) includes the circle. Why do the graphs look more and more square as n increases?
This function involves absolute values. To find the slope on the slide use different equations to define the function in different parts of its domain.
By sketching a graph of a continuous increasing function, can you prove a useful result about integrals?
Quadratic graphs are very familiar, but what patterns can you explore with cubics?
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.
Sketch the members of the family of graphs given by y = a^3/(x^2+a^2) for a=1, 2 and 3.
Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.
Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.
How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.
This problem challenges you to sketch curves with different properties.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
This task depends on learners sharing reasoning, listening to opinions, reflecting and pulling ideas together.
Can you make a curve to match my friend's requirements?
Several graphs of the sort occurring commonly in biology are given. How many processes can you map to each graph?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Explore how can changing the axes for a plot of an equation can lead to different shaped graphs emerging
Which line graph, equations and physical processes go together?
Which curve is which, and how would you plan a route to pass between them?
Explore the rates of growth of the sorts of simple polynomials often used in mathematical modelling.
Can you draw the height-time chart as this complicated vessel fills with water?
Can you match the charts of these functions to the charts of their integrals?
Can you massage the parameters of these curves to make them match as closely as possible?
What biological growth processes can you fit to these graphs?
If you plot these graphs they may look the same, but are they?
Compares the size of functions f(n) for large values of n.
This polar equation is a quadratic. Plot the graph given by each factor to draw the flower.
Plot the graph of x^y = y^x in the first quadrant and explain its properties.
The illustration shows the graphs of twelve functions. Three of them have equations y=x^2, x=y^2 and x=-y^2+2. Find the equations of all the other graphs.
Sketch the graph of $xy(x^2 - y^2) = x^2 + y^2$ consisting of four curves and a single point at the origin. Convert to polar form. Describe the symmetries of the graph.
Sketch the graphs for this implicitly defined family of functions.
In this 'mesh' of sine graphs, one of the graphs is the graph of the sine function. Find the equations of the other graphs to reproduce the pattern.
Show without recourse to any calculating aid that 7^{1/2} + 7^{1/3} + 7^{1/4} < 7 and 4^{1/2} + 4^{1/3} + 4^{1/4} > 4 . Sketch the graph of f(x) = x^{1/2} + x^{1/3} + x^{1/4} -x
Investigate the graphs of y = [1 + (x - t)^2][1 + (x + t^)2] as the parameter t varies.