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MAT091 :: Lecture Note :: Week 04
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An interval is a range of values that start with a minimum and end with a maximum.
Intervals can be represented using the following notation.
[min, max] where [ implies min is in the interval and ] implies max is in the interval (min, max] where ( implies min is not in the interval and ] implies max is in the interval [min, max) where [ implies min is in the interval and ) implies max is not in the interval (min, max) where ( implies min is not in the interval and ) implies max is not in the interval brackets imply end points are included parenthesis imply end points are excludedExamples.
[0, 5] implies all numbers between and including 0 and 5 (0, 5] implies all numbers greater than 0 and less than or equal 5
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An algebraic expression is a mathematical expresssion that contains at least one variable along with zero or more numbers (i.e. constants) and zero or more arithmetic operators.
The following are algebraic expressions.
n 3n 5n + 10 2x^2  2y^3 9a + 2b  3c 11(x + y^3 + 2w)Variables are unknown values that are represented by singlecharacter letters. For example,
3n
is3 times 'n'
, where 'n' is a variable. If a value is assigned to 'n', then the expression can be evaluated.3n + 8 if n = 3, then 3(3) + 8 = 100 if n = 5, then 3(5) + 8 = 7 if n = 0, then 3(0) + 8 = 8The replacement (or swapping) of variables with values can be described in a variety of ways: Values can be "plugged into" or "assigned to" variables; or variables can be "replaced with" or "substituted with" values; or we "let" variables be certain values.
5x + 1 assign 5 to x ........... 5(5) + 1 = 25 + 1 = 26 5x + 1 replace x with 5 ........ 5(5) + 1 = 25 + 1 = 26 5x + 1 plug 5 into x ........... 5(5) + 1 = 25 + 1 = 26 5x + 1 substitute x with 5 ..... 5(5) + 1 = 25 + 1 = 26 5x + 1 let x be 5 .............. 5(5) + 1 = 25 + 1 = 26Again, expressions are typically evaluated after variables have been assigned (i.e. given) values.
If a variable is multiplied by a constant, then the constant is called a coefficient.
3n ...... 'n' is a variable and 3 is a coefficient x ....... 'x' is a variable and 1 is the coefficient 1y ..... 'y' is a variable and 1 is the coefficientThe combination of a coefficent and variable is called a factor. Factors are numbers, variables, and expressions that are multiplied together to produce a product.
Factors separated by addition and subtraction operators are called terms.
3n + 1 .............. 1 factor, 2 terms 4a + 2b  10 ........ 2 factors (4a and 2b), 3 terms 7x  5 + 8y  11 .... 2 factors (7x and 8y), 4 terms 2x^3 + 10^2.......... 1 factor (2x^3), 2 terms 3(4)  2(1 + 3)...... 2 factors, 2 terms
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