Mat 171 Flashcards

Coordinate Systems and Functions

• Rectangular coordinate system is also known as the Cartesian coordinate system, used for graphing equations.
• An equation in two variables, such as y=3x-5, consists of an independent variable (x) and a dependent variable (y).
• Use parentheses for intervals when dealing with overlapping intervals or when open circles are present.

Area Formulas

• Area of a trapezium is calculated using the formula A = 1/2(a + b)h, where a and b are the lengths of the parallel sides.
• The area of a rhombus is determined by A = 1/2 x diagonal 1 x diagonal 2.
• The area of a circle is given by the formula A = πr², where r is the radius.
• Area of a sector of a circle can be calculated using A = (n/360)πr², where n is the angle in degrees.

Mathematical Concepts

• Mathematical modeling involves using equations to represent the relationships between different variables.
• An even function has symmetry with respect to the y-axis, characterized by the property f(x) = f(-x).
• An odd function displays symmetry concerning the origin, following the rule f(-x) = -f(x).

Reflections and Transformations

• The transformation f(-x) = -f(x) results in all components of the equation being sign-changed.
• Reflection about the x-axis transforms (x,y) to (-x,-y) by substituting -y into the equation.

Types of Functions

• A piecewise function is defined using two or more expressions corresponding to different intervals, which may be expressed with parentheses.
• A step function is represented graphically as a series of line segments rather than a continuous curve.

Linear Regression and Line Properties

• A regression line represents the line of best fit for a data set.
• The slope of a vertical line is undefined, while a horizontal line has a slope of m = 0.
• The point-slope form of a line is expressed as y - y₁ = m(x - x₁).
• The slope-intercept form is represented by y = mx + b, where m indicates the slope and b denotes the y-intercept.
• The general form of a linear equation is Ax + By + C = 0, useful for finding intercepts.

Relationship between Lines

• Parallel lines share the same slope.
• Perpendicular lines possess slopes that are negative reciprocals of each other.

Function Transformations

• The transformation f(x) -> -f(x) indicates reflection over the x-axis.
• The transformation f(x) -> f(-x) indicates reflection over the y-axis.
• A vertical stretch is achieved by multiplying all y-values of a function by a factor greater than 1.
• A vertical shrink compresses all y-values by a factor greater than 0 but less than 1.
• A horizontal stretch affects the x-values, typically involving multiplication by a factor less than 1.