Mat 171 Flashcards

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Questions and Answers

What is another name for the rectangular coordinate system?

Spherical coordinate system

Cylindrical coordinate system

Cartesian coordinate system (correct)

Polar coordinate system

What is an equation in two variables?

An equation that can be described with two variables, such as y=3x-5, where x is independent and y is dependent.

Use ( ) for intervals when it overlaps with another interval or there are open circles.

True

What is the formula for the area of a trapezium?

A = 1/2(a+b)h Signup and view all the answers

What is the area of a rhombus?

A = 1/2 x diagonal 1 x diagonal 2 Signup and view all the answers

What is the formula for the area of a circle?

A = πr² Signup and view all the answers

What is the area of a sector of a circle?

A = (n/360)πr² Signup and view all the answers

What is mathematical modeling?

Using equations to model the relationships between variables. Signup and view all the answers

What characterizes an even function?

The graph is symmetrical with respect to the y-axis; f(x) = f(-x). Signup and view all the answers

What characterizes an odd function?

The graph is symmetrical with respect to the origin; f(-x) = -f(x). Signup and view all the answers

What does the equation f(-x) = -f(x) imply?

All components of an equation change sign. Signup and view all the answers

What is reflection about the x-axis?

(x,y) -> (-x,-y) Signup and view all the answers

What is a piecewise function?

A function that is written using two or more expressions; intervals expressed with ( ). Signup and view all the answers

What defines a step function?

A function whose graph is a series of line segments. Signup and view all the answers

What is a regression line?

Line of best fit. Signup and view all the answers

What is the slope of a vertical line?

Undefined; #/0. Signup and view all the answers

What is the slope of a horizontal line?

m = 0. Signup and view all the answers

What is the point-slope form of a linear equation?

y - y1 = m(x - x1) Signup and view all the answers

What is the slope-intercept form of a linear equation?

y = mx + b, where m is the slope and b is the y-intercept. Signup and view all the answers

What is the general form of a linear equation?

Ax + By + C = 0. Signup and view all the answers

What characterizes parallel lines?

They have the same slope. Signup and view all the answers

What characterizes perpendicular lines?

They have negative reciprocal slopes. Signup and view all the answers

What does the equation f(x) -> -f(x) represent?

Reflection over the x-axis. Signup and view all the answers

What does the equation f(x) -> f(-x) represent?

Reflection over the y-axis. Signup and view all the answers

What is a vertical stretch?

Multiplies all y-values of a function by the same factor greater than 1. Signup and view all the answers

What is a vertical shrink?

Multiplies all y-values of a function by the same factor greater than 0 but less than 1. Signup and view all the answers

What does a horizontal stretch refer to?

<ol start="0"> <li></li> </ol> Signup and view all the answers

Study Notes

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.

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