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math 1st term

1. exponents

   • The exponent of a number says how many times to use the number in a multiplication.
     • Anything to the power zero is just 1.
   • negative exponents
     • A negative exponent means how many times to divide one by the number.
       • Example: 8-1 = 1 ÷ 8 = 0,125

2. logarithms

   • the logarithm is the inverse operation to exponentiation
     • Common Logarithm
       • A logarithm with base e is known as natural logarithm.
         • For example: loge4
           • e is a constant whose value is approximately 2.178
           • Natural logarithms are also represented as ln x.
     • Natural Logarithm
       • A logarithm with base 10 is known as common logarithm
         • For example: log104
           • We see log without any base very often.
             • It means that the base is 10
             • For example: log104 or log 4 are same

3. functions

   • domain
     • is all the values that x is allowed to take on.
       • State the domain and range of the following relation. Is the relation a function?
         • {(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}
         • domain: {2, 3, 4, 6}
         • range: {–3, –1, 3, 6}
   • range
     • is all the values that y is allowed to take on.
   • independent variable
   • dependent variable
     • In mathematics, the "x" and "y" values in an equation or a graph are referred to as "variables."
       • If an equation shows a relationship between x and y in which the value of y is dependent upon the value of x, y is known as the dependent variable.
         • is sometimes referred to as ‘function(x)’ or f(x).
       • The final solution of the equation, y, depends on the value of x, the independent variable which can be changed Read more at
   • graph
     • quadratic funtion
       • roots/zeros
         • an input value that produces an output of zero
       • y intercept
         • in question is given as y = f(x)
         • these points satisfy x = 0.
       • vertex
         • line of symmetry
         • lowest/highest point on Y
     • linear function
       • y intercept
       • slope
         • number that describes both the direction and the steepness of the line.
           • If a line is horizontal the slope is zero.
           • A line is decreasing if it goes down from left to right. The slope is negative
           • A line is increasing if it goes up from left to right. The slope is positive
         • Slope is often denoted by the letter m.

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