Class Notes Chapter 2

Class Notes Chapter 2 Relation -CORRECT ANSWER-correspondence between two sets. x corresponds to y & y depends on x x: independent, domain y: dependent, range Increasing Function -CORRECT ANSWER-A function f is increasing on an open interval I if, for any choice of x1 & x2 in I, with x1x2, we have f(x1)f(x2) Decreasing Function -CORRECT ANSWER-A function f is decreasing on an open interval I if, for any choice of x1 & x2 in I, with x1x2, we have f(x1)f(x2) Constant Function -CORRECT ANSWER-A function f is constant on an open interval I if, for any choice of x1 & x2 of , with x1x2, we hvae f(x1)=f(x2) Average Rate of Change -CORRECT ANSWER-If a & b, a not equal to b, are in the domain of function y=f(x), the average rate of change of f from a to b is defined as the change of y over the change in x =f(b)-f(a)/b-a Slope of a secant line -CORRECT ANSWER-ARC of a function f, from a to b, equals the slope of teh secant line containing the points (a, f(a)) and (b, f(b)) ARC = m_sec Extreme Value Theorem -CORRECT ANSWER-If f is a continuous functoin whose domain is a closed interval [a,b], then f has an absolute macimum and an absolute minimum The Greatest Integer Function -CORRECT ANSWER-The domain is all real numbers and the range is all integers y-intercept is 0 and the x intercept is [0,1) The function is neither even nor odd and has a discontinuity at every integer Piecewise-defined Functoins -CORRECT ANSWER-When functions are defined by more than one equation Transformatoins -CORRECT ANSWER-All the transformations of a function form a maily of functoins Shifting vertically -CORRECT ANSWER-If a real number k is added to the right side of a function y=f(x), the graph of the new function y=f(x)+k is the graph of f shifted vertically up k units (if k0) or down k units (if k0) Shifting horizontally -CORRECT ANSWER-If the argument x of a function is replaced by x-h, h0, the graph of the new function y=f(x-h) is the graph of f shifted horizontally right h units. If the argument of a function f is replaced by x+h, h0, the graph of the new function y=f(x+h) is the graph of f shifted horizontally left h units Transforming by Vertical stretch/compress -CORRECT ANSWER-When the right side of a function y=f(x) is multiplied by a positive number a, the graph of the new function of y=af(x) is obtained by multiplying each y-coordinate on the graph of y=f(x) by a. The new graph is vertically compressed (if -a1) or vertically stretched(if a1) Transforming by Horizontal stretch/compress -CORRECT ANSWER-If the argument x of a function y=f(x) is multiplied by a positive number a, the graph of the new function y=f(ax) is obtained by multiplying each x-coordinate of y=f(x) by 1/a. A horizontal compression results if a1, and a