Other tags that relate to Tangled Trig Graphs
Inequalities. Symmetry. Maths Supporting SET. Trigonometric functions and graphs. Graph sketching. Turning points. Biology. Graphing software and graphical calculators. Transformation of functions. Functions and their inverses.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.
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.
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.
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.
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?
Cocked Hat
Age 16 to 18
Challenge Level
Sketch the graphs for this implicitly defined family of functions.
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.
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?
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.
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.
Curve Fitter
Age 14 to 18
Challenge Level
This problem challenges you to find cubic equations which satisfy different conditions.
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.
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?
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.
Curve Hunter
Age 14 to 18
Challenge Level
This problem challenges you to sketch curves with different properties.
Exploring Cubic Functions
Age 14 to 18
Challenge Level
Quadratic graphs are very familiar, but what patterns can you explore with cubics?
Scientific Curves
Age 16 to 18
Challenge Level
Can you sketch these difficult curves, which have uses in mathematical modelling?
What's That Graph?
Age 14 to 18
Challenge Level
Can you work out which processes are represented by the graphs?
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?
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?
Spot the Difference
Age 16 to 18 Short
Challenge Level
If you plot these graphs they may look the same, but are they?
Back Fitter
Age 14 to 18
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?
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?
How Does Your Function Grow?
Age 16 to 18
Challenge Level
Compares the size of functions f(n) for large values of n.
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
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.
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?
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.