Get Advanced Functions PDF
By Chris Kirkpatrick, Marian Small, Barbara Alldred
Constructed for the ON Grade 12 complex services Curriculum MHF4U, Revised 2007. beneficial properties & merits include:
• complete, digital model of the scholar textual content on CD, in PDF format
• bankruptcy Openers with talents and suggestion Reviews
• Getting all started, together with assessment of key vocabulary, key recommendations, and understandings
• Mid-Chapter and bankruptcy reports with commonly asked Questions
• a number of solved examples with causes combine the mathematical process
• big variety of perform questions progressively expanding in difficulty
• pattern fulfillment Chart classification questions pointed out in each lesson
• precis of Key rules and ideas in each lesson
• expertise help comprises: TI-83 Plus, TI-84 Plus, The Geometer's Sketchpad®, Spreadsheets, TI-Nspire CAS Handhelds
• unfastened on-line entry to applets and different sensible eTools that deliver the maths to existence
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Additional resources for Advanced Functions
5 Inverse Relations 4000 Volume (cm3) 3500 Radius is the independent variable, and volume is the dependent variable. 3000 2500 Create a table of values, and calculate the volume for a specific radius. 2000 1500 Draw a scatter plot of volume in terms of radius. Draw a smooth curve through the points since the function is continuous. 0 8 To graph radius in terms of volume, switch the variables in the table, making radius the dependent variable and volume the independent variable. 6 4 2000 4000 6000 Volume (cm3) 16 y 12 y=x 8 4 –4 0 –4 The red curve shows volume as the independent variable and radius as the dependent variable.
C. How do you determine from a graph or from the algebraic representation of a piecewise function if there are any discontinuities? APPLY the Math EXAMPLE 3 Representing a piecewise function using a graph Graph the following piecewise function. f (x) 5 e x 2, if x , 2 2x 1 3, if x $ 2 Solution Create a table of values. 6 Piecewise Functions f (x) 5 2x 1 3 x f(x) x f(x) 22 4 2 7 21 1 3 9 0 0 4 11 1 1 5 13 2 4 6 15 From the equations given, the graph consists of part of a parabola that opens up and a line that rises from left to right.
A) Sketch the graph of the piecewise function. b) Describe the continuity of the function. c) How many fish were killed by the chemical spill? d) At what time did the population recover to the level it was before the chemical spill? e) Describe other events relating to fish populations in a lake that might result in piecewise functions. 6 10. Create a flow chart that describes how to plot a piecewise function with two pieces. In your flow chart, include how to determine where the function is continuous.
Advanced Functions by Chris Kirkpatrick, Marian Small, Barbara Alldred