Resources tagged with: Graph sketching

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There are 41 results

Broad Topics > Coordinates, Functions and Graphs > Graph sketching

Guess the Function

Age 16 to 18 Challenge Level:

This task depends on learners sharing reasoning, listening to opinions, reflecting and pulling ideas together.

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.

Rational Request

Age 16 to 18 Challenge Level:

Can you make a curve to match my friend's requirements?

Curve Match

Age 16 to 18 Challenge Level:

Which curve is which, and how would you plan a route to pass between them?

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?

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?

Pitchfork

Age 16 to 18 Challenge Level:

Plot the graph of x^y = y^x in the first quadrant and explain its properties.

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.

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.

Cocked Hat

Age 16 to 18 Challenge Level:

Sketch the graphs for this implicitly defined family of functions.

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.

Age 16 to 18 Challenge Level:

Compares the size of functions f(n) for large values of n.

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.

Equation Matcher

Age 16 to 18 Challenge Level:

Can you match these equations to these 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?

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.

Scientific Curves

Age 16 to 18 Challenge Level:

Can you sketch these difficult curves, which have uses in mathematical modelling?

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.

Curvy Catalogue

Age 16 to 18 Challenge Level:

Make a catalogue of curves with various properties.

Integration Matcher

Age 16 to 18 Challenge Level:

Can you match the charts of these functions to the charts of their integrals?

Brimful

Age 16 to 18 Challenge Level:

Can you find the volumes of the mathematical vessels?

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.

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.

Exploring Cubic Functions

Age 14 to 18 Challenge Level:

Quadratic graphs are very familiar, but what patterns can you explore with cubics?

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.

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?

Reaction Types

Age 16 to 18 Challenge Level:

Explore the rates of growth of the sorts of simple polynomials often used in mathematical modelling.

Whose Line Graph Is it Anyway?

Age 16 to 18 Challenge Level:

Which line graph, equations and physical processes go together?

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?

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

Maths Filler 2

Age 14 to 16 Challenge Level:

Can you draw the height-time chart as this complicated vessel fills with water?

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 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?

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?

Bio Graphs

Age 14 to 16 Challenge Level:

What biological growth processes can you fit to these graphs?

What's That Graph?

Age 14 to 16 Challenge Level:

Can you work out which processes are represented by the graphs?

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?

How Many Solutions?

Age 16 to 18 Challenge Level:

Find all the solutions to the this equation.

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.