Does the set span R3?

Chapter 1: Sections 1-6 1.1 What is a Function A function is a rule that takes certain numbers as inputs and assigns to each a definite output number. Domain: the set of all input numbers Range: the set of all output numbers Independent Variable: input Dependent Variable: output Interval Notation: Closed Intervals: a ⦤ t ⦤b and is written [a,b] Open Intervals: a < t < b and is written (a,b) A mathematical model is a mathematical description of a real situation. Increasing and Decreasing Functions: A function is increasing if the values of f(x) increase as x increases A function is decreasing if the values of f(x) decrease as x increases 1.2 Linear Functions A linear function has a graph that has a straight line. Slope= rise/run = ∆y/∆x= f(x2)-f(1 )2x 1x A linear function has the form y=b+mx If m is positive, f(x) is increasing. If m is negative, f(x) is decreasing. If m is 0 we have a straight line. 1.3 Average Rate of Change and Relative Change Visualizing Rate of Change The change in a function( ∆y) is represented by a vertical distance. The average rate of change (blue line) is represented by the slope of a line. Concavity Concavity is a way of classifying a graph. Concave Up: Concave Down: Relative Change In general, when a quantity P changes from P to P0 1 Relative change in P= change in P/ P = P0- P 1 P 0 0 You can remember it like a cup. If is could hold water, it is concave up. If it cannot, it is concave down.