What are key properties of functions?

Key questions

  1. 1

    What is a function and what are some examples of functions?

  2. 2

    What features of functions are visible on a graph?

  3. 3

    What is an asymptote and what are some functions which have them?

  4. 4

    What does the graph of the absolute value or modulus function look like?

  5. 5

    What do we mean by symmetry of a function?

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Resource type Title
Rich example What relation are you?
Building blocks Approaching asymptotes
Building blocks That's odd ... or even
Package of problems Mapping a function
Problem requiring decisions Piece it together
Investigation Absolutely!


Resource type Title
Fluency exercise Odd or even or...
Package of problems Inequality flip-flop
Many ways problem Function squares
Many ways problem Two-way functions
Scaffolded task Worth 1000 words
Food for thought Curve match
Food for thought Picture the process I
Resource in action Two-way functions - teacher support

Review questions

Title Ref
Can we sketch the graph of $y = |x| + |x-1| + |x-4|$? R9130
Can we sketch this function with its asymptotes? R5559
Can we sketch this periodic, parabolic function? R8027
Can we solve this inequality involving two modulus functions? R9896
How many roots does this equation have? R6896
What are the greatest and least values of $f(x) - g(x)$ on this interval? R9056
When is one of these functions greater than the other? R6008
Where does the graph of this modulus function cross $y = 1/x$? R8079
Where is $|x|$ less than $|y|$? R6392