A jewelry maker has total revenue for her necklaces given by R(x)=90.75x, and incurs a total cost of C(x)=24.50x+4770, where x is the number of necklaces produces and sold. How many necklaces must be produced and sold in order to break even?

Features of Graphs of FunctionsThinking with your fingers

TerminologyIncreasing As your x finger moves right, your y finger moves up.Decreasing As your x finger moves right, your y finger moves downConstant As your x finger moves right, your y finger does not move

Because x is the independent variable, increasing/decreasing/constant intervals are described in terms of values of xThinking with your fingers

Interval Notation

Increasing on (-,-2)Decreasing on (-2,2)Increasing on (2,)Extrema and Local ExtremaThe maximum of a graph is its highest y value.The minimum of a graph is its lowest y value.A local maximum of a graph is a y value where the graph changes from increasing to decreasing. (Stops getting bigger)A local minimum of a graph is a y value where the graph changes from decreasing to increasing (Stops getting smaller)These extrema are all y values. But because x is the independent variable, they are often described by their location (x value).

Extrema

No minimum, or minimum of -No maximum, or maximum of Local maximum of (x)=5.3333at x=-2Local minimum of (x)=-5.3333at x=2Using your graphing utility, graph the function below and determine on which x-interval the graph of h(x) is increasing:

Using your graphing utility, graph the function below and determine on which x-interval the graph of h(x) is increasing:

Piecewise FunctionsThe Bank ProblemFrances puts $50 in a bank account on Monday morning every week.Draw a graph of what Frances's bank account looks like over time. Put number of weeks on the horizontal axis, and number of dollars in her account on the vertical axis.

Frances Bank Account

Writing a formula for Frances

Piecewise functionFunction definition is given over interval pieces

Ex:

Means: When x is between 0 and 2, use the formula 2x+1. When x is between 2 and 5, use the formula (x-3)2

ExampleFind (3)Check the first condition: 03