Other tags that relate to Tangled Trig Graphs
Graphing software and graphical calculators. Symmetry. Maths Supporting SET. Biology. Limits of Sequences. Inequalities. Turning points. Functions and their inverses. Graph sketching. Trigonometric functions and graphs.There are 42 results
Broad Topics > Coordinates, Functions and Graphs > Graph sketching
Tangled Trig Graphs
Age 16 to 18 Challenge Level:
Can you work out the equations of the trig graphs I used to make my pattern?
Quartics
Age 16 to 18 Challenge Level:
Investigate the graphs of y = [1 + (x - t)^2][1 + (x + t^)2] as the parameter t varies.
Maltese Cross
Age 16 to 18 Challenge Level:
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.
Curve Match
Age 16 to 18 Challenge Level:
Which curve is which, and how would you plan a route to pass between them?
Parabolic Patterns
Age 14 to 18 Challenge Level:
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.
Rational Request
Age 16 to 18 Challenge Level:
Can you make a curve to match my friend's requirements?
Guess the Function
Age 16 to 18 Challenge Level:
This task depends on learners sharing reasoning, listening to opinions, reflecting and pulling ideas together.
Pitchfork
Age 16 to 18 Challenge Level:
Plot the graph of x^y = y^x in the first quadrant and explain its properties.
Area L
Age 16 to 18 Challenge Level:
By sketching a graph of a continuous increasing function, can you prove a useful result about integrals?
A Close Match
Age 16 to 18 Challenge Level:
Can you massage the parameters of these curves to make them match as closely as possible?
Squareness
Age 16 to 18 Challenge Level:
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?
More Parabolic Patterns
Age 14 to 18 Challenge Level:
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.
Slide
Age 16 to 18 Challenge Level:
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.
Folium of Descartes
Age 16 to 18 Challenge Level:
Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.
Cocked Hat
Age 16 to 18 Challenge Level:
Sketch the graphs for this implicitly defined family of functions.
Witch of Agnesi
Age 16 to 18 Challenge Level:
Sketch the members of the family of graphs given by y = a^3/(x^2+a^2) for a=1, 2 and 3.
Spot the Difference
Age 16 to 18 Short Challenge Level:
If you plot these graphs they may look the same, but are they?
Exploring Cubic Functions
Age 14 to 18 Challenge Level:
Quadratic graphs are very familiar, but what patterns can you explore with cubics?
Graphic Biology
Age 16 to 18 Challenge Level:
Several graphs of the sort occurring commonly in biology are given. How many processes can you map to each graph?
How Does Your Function Grow?
Age 16 to 18 Challenge Level:
Compares the size of functions f(n) for large values of n.
Sine Problem
Age 16 to 18 Challenge Level:
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.
Power Up
Age 16 to 18 Challenge Level:
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
Integration Matcher
Age 16 to 18 Challenge Level:
Can you match the charts of these functions to the charts of their integrals?
Scientific Curves
Age 16 to 18 Challenge Level:
Can you sketch these difficult curves, which have uses in mathematical modelling?
Polar Flower
Age 16 to 18 Challenge Level:
This polar equation is a quadratic. Plot the graph given by each factor to draw the flower.
Whose Line Graph Is it Anyway?
Age 16 to 18 Challenge Level:
Which line graph, equations and physical processes go together?
Reaction Types
Age 16 to 18 Challenge Level:
Explore the rates of growth of the sorts of simple polynomials often used in mathematical modelling.
Ideal Axes
Age 16 to 18 Challenge Level:
Explore how can changing the axes for a plot of an equation can lead to different shaped graphs emerging
Bio Graphs
Age 14 to 16 Challenge Level:
What biological growth processes can you fit to these graphs?
Mathsjam Jars
Age 14 to 16 Challenge Level:
Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?
Bird-brained
Age 16 to 18 Challenge Level:
How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.
Back Fitter
Age 14 to 16 Challenge Level:
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?
Immersion
Age 14 to 16 Challenge Level:
Various solids are lowered into a beaker of water. How does the water level rise in each case?
Maths Filler 2
Age 14 to 16 Challenge Level:
Can you draw the height-time chart as this complicated vessel fills with water?
Guessing the Graph
Age 14 to 16 Challenge Level:
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
What's That Graph?
Age 14 to 16 Challenge Level:
Can you work out which processes are represented by the graphs?
Interpolating Polynomials
Age 16 to 18 Challenge Level:
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.
NRICH is part of the family of activities in the Millennium Mathematics Project.