Chapter 2 Functions and graphs - Year 2 Flashcards
What does this graph look like?
What happens if you start to transform it? (Simple translations)
As you move the graph around the y axis will mirror what is on the x axis
Also the x axis will mirror what is on the y axis
(So you will always know the y intercept and where it cuts or touches the x axis)
How do you draw a mod graph?
Method 1) Draw the normal graph (without the mods) then reflect whatever is below the x axis into the positive x plane
How do you solve modulus problems?
You need to draw them out to see where the interceptions are
Then you need to:(if the answer is in the non reflected bit delete the mods and solve normally)
(If the answer is in the reflected bit then negative whatever is in the modulus, then solve normally)
What is the domain of a function?
The posible inputs into a function
(Vertical lines)
What is the range of a function?
The set of all posible solutions to a function
What is a function?
A function is a special type of mapping such that each member of the domain is mapped to 1 and only 1 element in the range
What do I always forget to do when writing the range of a function?
I forget tp say f(x) and not x
What are the different types of mappings?
Many to 1
1 to many
1 to 1
What type of mapping is a function?
1 to 1
What type of mapping is a quadratic?
Many to 1
What is a piecewise functon?
A function which is defined in parts so we can use different rules for different intervals of the range
What do you do with a piecewise function at the point in which 1 graph stops and the other begins?
You literally stop (draw a little circle to represent the fact that that point isn’t included in the graph and then start drawing the next graph.
If the domain has an (less or grater) than AND equal to then you colour in the circle to show that
How do you work out a composite function in terms x?
You substitute the latter function into the primary function (wherever there is an x)
What must be true about a function for it to have an inverse function?
Why?
It must be 1 to 1 for an inverse function to exist
Because if the mapping was many to 1 then the inverse mapping would be 1 to many but this is nit a function
What is the method to find the inverse of a function
Put it equal to y then re arranged to make x the subject
What do you need to remember to do when working out the inverse function?
Write the inverse function out in terms of x
How do you find the inverse function of y=a quadratic?
You complete the square on the quadratic
What are 3 useful facts about inverse functions?
They do the opposite of the original function
They are a mirror of the original function in the line y=x so any solutions to the equation will be on the line y=x
The domain of the function = the range of the inverse function
The range of the function = the domain of the inverse function
When doing questions in all topics what do you need to be mindful about your answers?
If the question states the domain only that part of the graph matters. If there are solutions which are outside the domain/range then they don’t matter
(Could calculations need to stay within the domain)
How do you draw a graph of
Draw the normal graph and then anything below the x axis is reflected above it
How do you draw a graph of
You reflect it in the y axis
What is a common mistake when solving modulus questions?
People negative everything but you are only supposed to negative the mod bit
In which order do you do the transformations?
