Graph sketching

There are 48 NRICH Mathematical resources connected to Graph sketching
Exploring cubic functions
problem
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Exploring cubic functions

Age
14 to 18
Challenge level
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Quadratic graphs are very familiar, but what patterns can you explore with cubics?

Area L
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Area l

Age
16 to 18
Challenge level
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By sketching a graph of a continuous increasing function, can you prove a useful result about integrals?
Immersion
problem
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Immersion

Age
14 to 16
Challenge level
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Various solids are lowered into a beaker of water. How does the water level rise in each case?
Tangled Trig Graphs
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Tangled trig graphs

Age
16 to 18
Challenge level
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Can you work out the equations of the trig graphs I used to make my pattern?

Slide
problem
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Slide

Age
16 to 18
Challenge level
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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.
Squareness
problem
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Squareness

Age
16 to 18
Challenge level
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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?
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How many solutions?

Age
16 to 18
Challenge level
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Find all the solutions to the this equation.
How far does it move?
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How far does it move?

Age
11 to 14
Challenge level
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Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects the distance it travels at each stage.

Back fitter
problem
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Back fitter

Age
14 to 18
Challenge level
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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?

Speeding up, slowing down
problem
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Speeding up, slowing down

Age
11 to 14
Challenge level
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Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its speed at each stage.