Algebra II Ch. 2 Concepts
Parent Function
A family of functions is a group of functions with shared characteristics. The parent function is the most basic function in a family.
Function
A function is a relation for which each input has exactly one output. If any input of a relation has more than one output, the relation is not a function.
Relation
A relation is a mapping, or pairing, of input values with output values.
Slope-Intercept Form
If you write the equations as y = 2x +0 and y = 1x+3, you can see that the x-coefficients, 2 and 1, are the slopes of the lines, while the constant terms, 0 and 3, are the y-intercepts. In general, a lines with equation y = mx+b has slope m and y-intercept b. The equation y = mx+b is said to be in slope-intercept form.
Y-Intercept
In general, a y-intercept of a graph is the y-coordinate of a point where the graph intersects the y-axis.
Equation in Two Variables
Many functions can be described by an equation in two variables, such as y=3x-5. The input variable (in this case x) is called the independent variable. The output variable (in this case y) is called the dependent variable because its value depends on the value of the input variable.
Parallel and Perpendicular Lines
Recall that two lines in a plane are parallel if they do not intersect. Two lines in a plane are perpendicular if they intersect to form a right angle. Slope can be used to determine whether two different non vertical lines are parallel or perpendicular.
Rate of Change
Slope can be used to represent an average rate of change, or how much one quantity changes, on average, relative to the change in another quantity. A slope that is a real-life rate of change involves units of measure such as miles per hour or degrees per day.
Linear Function and Function Notation
The function y=-2x-1 is a linear function because it can be written in the form y=mx+b where m and b are constants. The graph of a linear function is a line. By renaming y as f(x), you can write y=mx+b using function notation.
Domain and Range
The set of input values is the domain, and the set of output values is the range.
Slope
The slope m of a non vertical line is the ratio of vertical change (the rise) to horizontal change (the run).
Classification of Lines by Slope
The slope of a line indicates whether the line rises from left to right, falls from left to right, is horizontal, or is vertical. A positive slope rises from left to right, a negative slope falls from left to right, a zero slope is horizontal, and an undefined slope is vertical.
Standard Form and X-Intercept
The standard form of a linear equation is Ax + By = C where A and B are not both zero. You can graph an equation in standard form by identifying and plotting the x and y intercepts. An x-intercept is the x-coordinate of a point where a graph intersects the x-axis.
