Key Terms and Equations

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Key Terms

Function- A function is a rule that takes certain numbers as inputs and assigns to each a definite output number.

Domain- The domain of a function is the set of all input numbers. The input is called the independent variable, and is usually represented by x values.

Range- The range of a function is the set of all output numbers. The output is called the dependent variable, and is usually represented by y values.

Example- y = x^2 is an example of a function. The domain for this function is all real numbers, and the range for this function is y must be greater than or equal to zero.


Linear Function- A linear function has the form y = mx + b. Its graph is a line such that m is the slope, or rate of change of y with respect to x, and b is the y-intercept, or value of y when x is zero.

Example- Here is an example of a linear function with a slope of 3/4 and a y intercept of 1. The equation of the line is y = 0.75x + 1.

Y = .75x + 1

Exponential Functions- An exponential function is a function with the input variable (x) in the exponent. Exponential functions are of the form y = y0*a^x where y0 is the initial quantity (when x = 0) and a is the factor by which y changes when x increases by 1. If a is greater than 1, there is exponential growth. If a is between 0 and 1, there is exponential decay.

Examples- The following graphs depict examples of exponential growth and exponential decay. 2^x Exp decay

Continuous Exponential Growth/Decay- Continuous exponential growth and decay can be expressed by exponential functions with the base e. The standard format of such functions is y=y0*e^kx, where y0 is the initial quantity and k is the rate of growth or decay. If k is greater than 0, there is exponential growth. If k is less than 0, there is exponential decay. Example- Here is a graph of y=e^x, which represents continuous exponential growth.


Helpful Equations

Linear Funcions- y = mx + b

Slope of a line- m = (y2 - y1)/(x2 - x1)

Distance Formula- The distance between any two points (x1, y1) and (x2, y2) is D^2=(x2-x1)^2 + (y2-y1)^2

Quadratic Formula- If ax^2+bx+c = 0, then Quad form

Circles- With a center (h,k) and a radius r, (x-h)^2 + (y-k)^2 = r^2. Area of a circle: A = pi*r^2. Circumference of a circle: C = 2*pi*r.

Triangle- Area of a triangle: A = (1/2)*b*h.

Sphere- Volume of a sphere: V=(4/3)*pi*r^3. Area of a sphere: A = 4*pi*r^2

Cylinder- Volume of a cylinder: V = pi*r^2*h.

Cone- Volume of a cone: V=(1/3)*pi*r^2*h.

Useful Links

The following links may be helpful in your exploration of mathematical concepts.

The Math Forum is run by Drexel University, and offers many resources, including math help, problems and puzzles, and useful resources and tools.

Math is Fun is a website offering many math resurces, organized by course topic.

Math Mistakes is a website with real student mistakes on common math problems as well as correct solutions. The site also offers useful facts for Algebra, Trigonometry, and Calculus.

Analyze Math is a wonderful site with tons of useful information and resources, including tutorials for several subjects, sample problems and solutions with applets, example graphs, and printable worksheets.

Zona Land has specific sections focused on functions, geometry, and trigonometry. There is also a very useful data graphing tool which can be used to graphically represent sets of data.

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