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Unit 3: Functions (Inverse (Substitute X and Y., Make Y the subject, Solve…
Unit 3: Functions
Inverse
Substitute X and Y.
Make Y the subject
Solve the equation.
Quadratic Functions - roots and solutions
2 roots
2 solutions
Δ > 0
1 root
1 solution
Δ = 0
0 roots
No solution
Δ < 0
Domain and Range
Domain
All possible values of X.
Why do we restrict the domain?
You can not divide by 0.
Example: f(x) = 2/x -> Domain x ∈ ℝ ≠ 0
You can not take the square root of a negative number.
Example: f(x) = √x-6 -> Domain x ∈ ℝ ≠ 6
You can not take the logarithm of a negative number.
Range
All possible values of Y.
How do we find the range?
Look at the graph.
Look at the calculator.
Do the table.
Give X a value and complete the table for Y.
The value Y is getting near to, but never reaches is the range.
Example:
The range is -3.
Composition
f(x) and g(x) create together fg(x) or fog(x)
To create fg(x):
You substitute all values of X in f(x) with g(x).
Example:
To create gf(x):
You substitute all values of X in g(x) with f(x).
Example:
Sometimes the X becomes a number.
You need to solve the equation.
Example:
Transformation
Up and Down
f(x) -> f(x) + a
Up -> +
Down -> -
Example:
Left and Right
f(x) -> f(x - a)
Right -> -
Left -> +
Example:
Asymptotes
Vertical
The value that makes the denominator equal to 0.
Horizontal
The value that Y is reaching (in the table - range).
