PreCalculus M 117 A, Chapter 3 zContemporary Precalculus, 3rd edtion y- Thomas W. Hungerford zBr. Joel Baumeyer, F.S.C. zChristian Brothers University

Steps in Solving Word Problems

Working Definition of Function: H = f(t) nA function is a rule (equation) which assigns to each element of the domain (x value or independent variable) one and only one element of the range (y value or dependent variable). nDomain is the set of all possible values of the independent variable (x). nRange is the corresponding set of values of the dependent variable (y).

General Types of Functions(Examples): nLinear: y = m(x) + b; proportion: y = kx nPolynomial: Quadratic: y =x 2 ; Cubic: y= x 3 ; etc nPower Functions: y = kx p

Graph of a Function: nThe graph of a function is all the points in the Cartesian plane whose coordinates make the rule (equation) of the function a true statement.

Slope zm - slope : b: y-intercept za: x-intercept z.

5 Forms of the Linear Equation zSlope-intercept: y = f(x) = b + mx zSlope-point: zTwo point: zTwo intercept: zGeneral Form: Ax + By = C

Basic Facts for Straight Lines and Their Slopes zIf two lines have the same slope, they are parallel; i.e. m 1 = m 2 zTwo lines are perpendicular if the product of their slopes is -1; i.e. m 1 m 2 = -1 zA horizontal line has a slope of 0 and has an equation of the form: y = b. zA vertical line has an undefined slope and an equation of the form: x = c.

Making New Functions from Old Given y = f(x): (y - b) =k f(x - a) stretches f(x) if |k| > 1 shrinks f(x) if |k| < 1 reverses y values if k is negative a moves graph right or left, a + or a - b moves graph up or down, b + or b - If f(-x) = f(x) then f is an “even” function. If f(-x) = -f(x) then f is an “odd” function.

Average Rate of Change- The average rate of change is the slope of the secant line to two points on the graph of the function.

Inverse Functions: zTwo functions z = f(x) and z = g(x) are inverse functions if the following four statements are true: zDomain of f equals the range of g. zRange of f equals the domain of g. zf(g(x)) = x for all x in the domain of g. zg(f(y)) = y for all y in the domain of f.