How can a vertical asymptote of a rational function be found from the equation?
Vertical asymptotes can be found by first writing the function in factored form and then simplifying, i.e.: canceling out factors common to the numerator denominator. Once this is done the denominator is set to equal 0. The value of x obtained is the x-value of a vertical asymptote. There may be more than one.
Compare and contrast the concepts of range and standard deviation.
Range and Standard deviation are both measures of variability of a data set. This means they carry information as to how spread out the values are. Range is simpler to calculate: it is just the difference between the maximum and minimum values. Standard deviation is more complex to calculate and it represents the typical deviation from the mean.
Explain how slope (or rate of change) can be seen in each of the following representations of a linear function. (1) Table of Values (2) Graph (3) Equation
In the table of values, the slope is the amount that the dependent variable (y) changes as the independent variable (x) increase by 1. In the graph, the slope is the ratio of rise (vertical change) to run (horizontal change). In the equation, the slope is the coefficient of the term with the independent variable (x).