# Resources tagged with: Graph sketching

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### There are 41 results

Broad Topics > Coordinates, Functions and Graphs > Graph sketching

### 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.

### How Many Solutions?

##### Age 16 to 18 Challenge Level:

Find all the solutions to the this equation.

### 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?

### Spot the Difference

##### Age 16 to 18 Short Challenge Level:

If you plot these graphs they may look the same, but are they?

### 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.

### Cocked Hat

##### Age 16 to 18 Challenge Level:

Sketch the graphs for this implicitly defined family of functions.

### 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

### Pitchfork

##### Age 16 to 18 Challenge Level:

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

### 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.

### 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.

### Exploring Cubic Functions

##### Age 14 to 18 Challenge Level:

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

### 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.

### Guess the Function

##### Age 16 to 18 Challenge Level:

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

### Rational Request

##### Age 16 to 18 Challenge Level:

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

### 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.

### 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?

### 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?

### Curve Match

##### Age 16 to 18 Challenge Level:

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

### 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.

### 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.

### 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.

### 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.

### 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

### What's That Graph?

##### Age 14 to 16 Challenge Level:

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

### How Does Your Function Grow?

##### Age 16 to 18 Challenge Level:

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

### 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?

### Equation Matcher

##### Age 16 to 18 Challenge Level:

Can you match these equations 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?

### 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?

### Brimful

##### Age 16 to 18 Challenge Level:

Can you find the volumes of the mathematical vessels?

### 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?

### 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?

### Bio Graphs

##### Age 14 to 16 Challenge Level:

What biological growth processes can you fit to these graphs?

### 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?

### Maths Filler 2

##### Age 14 to 16 Challenge Level:

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

### Scientific Curves

##### Age 16 to 18 Challenge Level:

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

### Integration Matcher

##### Age 16 to 18 Challenge Level:

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