Functions KUS objectives BAT understand definition of a
Functions • • KUS objectives BAT understand definition of a function as a one to one mapping BAT recognise odd and even functions BAT state the domain and range of functions Evaluate f(2), f(-2), f(0) and f(-5) Which value of f(c) has no solution ? Evaluate f(2 x), f(x+3), and f(x-3)
Notes Domain and Range – mappings Instead of finding a single value of f(x) imagine that each number in the set of possible x values is Input to the function: - the corresponding outputs can be represented as a mapping as shown DOMAIN RANGE Because each element in the first set is mapped to exactly one output we say this mapping is one to one
Notes Domain and Range – mappings Consider this mapping DOMAIN RANGE Because some elements in the first set are mapped to the same output we say this mapping is many to one What other types of mappings can we have? Can you think of any operations that are one to many?
WB 1 a Domain and Range – graphically state the domain and range
Domain: The domain is the set of all possible x-values which will make the function "work", and will output real y-values. Range: The range is the resulting y-values we get after substituting all the possible x-values Sketch a graph to help figure it out Range Domain
WB 1 b Domain and Range – graphically state the domain and range
WB 3 ab Domain and Range – graphically Sketch each graph and state its domain and range
WB 3 cd Domain and Range – graphically Sketch each graph and state its domain and range
Notes Problems with one to many
Notes Problems with one to many: geogebra file ‘root (x+a)’
KUS objectives BAT understand definition of a function as a one to one mapping BAT recognise odd and even functions BAT state the domain and range of functions self-assess One thing learned is – One thing to improve is –
END
- Slides: 18