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Function Notation:
e.g. Given f(x) = 3x + 1, find f(2).
Slope and y-Intercept of a Line:
Given y = mx + b, the slope is ‘m’ and the y-intercept is ‘b’.
e.g. Find the slope and y-intercept of the function y – 2 = 3(x – 1)
Equation of a Line:
Slope-intercept form
Standard form
e.g. Determine the equation a the line that passes through the point (3, -2) and has a slope of -2.
Finite Differences:
This is a method to determine the type of function you have been given.
If the first difference is the same then it is linear. If the second difference is the same then it is quadratic, if the third difference is the same then it is a cubic function.
e.g.
Domain and Range:
e.g. State the domain and range of the function y = x2 + 2 in two different ways.
Quadratic Functions:
These are functions of the form y = a(x – p)2 + q. The vertex is the point (p,q) and ‘a’ determines the direction of opening.
e.g. Determine the vertex, direction of opening, domain and range of the function y = -3×2 + 6x – 2 and graph the function.
Transformations:
Functions can be transformed in the following ways: vertical and horizontal translations, stretches, or reflections.
e.g. Describe the transformations that must be applied to f(x) = x to get the function g(x) = -2f(x + 3) + 1.