P.() Functions. The student uses process standards in mathematics to eplore, describe, and analyze the attributes of The student makes connections between P.(G) graph functions, including eponential, logarithmic, sine, cosine, rational, and power functions and their transformations, including af(), f() + d, f( - c), f(b) for specific values of a, b, c, and d, in mathematical and realworld problems. Write equations of functions given transformations of parent functions and/or from the graph. Describe the transformations of a given equation written in translated form. Perform transformations utilizing the parent functions to sketch the graph of Write an equation for the function in the shape of f() =, but shifted si units to the left, si units down, and then reflected in the y-ais. Answer: f() = (-(+6)) 6 Reflection Transformation Vertical Shrink Vertical Stretch Link to ELPS Instructional : http://ritter.tea.state.t.us/rules/ta c/chapter074/ch074a.html 5B, B, D Students will be given different parent functions and all students will perform same transformation to their functions and then compare results. Section.6,.7 Parent Functions Charades The graph of y f ( ) is shown in the figure above. Which of the following could be the graph of y f ( )? A. B. *C. D. E. Last Edit 07-08 Page
P.(D) describe symmetry of graphs of even and odd Verify even and odd symmetry using algebraic procedures (such as substitution) and eplain your reasoning. Verify symmetry about the - ais, y-ais and origin utilizing algebraic techniques (substitution) and graphically. Which of the following equations has a graph that is symmetric with respect to the origin? A. y 5 *B. y C. 4 y 6 D. y E. y Even functions Odd functions Symmetry Link to ELPS Instructional : http://ritter.tea.state.t.us/rules/ta c/chapter074/ch074a.html 5B, 5C Use algebraic tests for symmetry using substitution to classify even and odd Have students classify functions by observing the graphs and their reflective properties. Section. Section.5 Even/Odd Functions P.() Functions. The student uses process standards in mathematics to eplore, describe, and analyze the attributes of The student makes connections between P.(I) determine and analyze the key features of eponential, power, trigonometric, inver se trigonometric, and functions, including step functions such as domain, range, symmetry, relative maimum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing. Determine domain and range of functions from equations and graphs. Evaluate functions, including piecewise Utilize graphs, tables & symbols If the domain of the function f given by f( ) is :, what is the range of f? A. y: y *B. y: y 0 C. y: y D. y: y E. y:0 y Dependent Variable Domain Function Independent Variable Piecewise Functions Range Relation Students will brainstorm and come up with ideas on what will affect the domain such as the denominator not equaling zero and radicals Section.4 Characteristics of Discontinuous Piecewise Functions Last Edit 07-08 Page
P.() Functions. The student uses process standards in mathematics to eplore, describe, and analyze the attributes of The student makes connections between P.(I) determine and analyze the key features of eponential, power, trigonometric, in verse trigonometric, and functions, including step functions such as domain, range, symmetry, relative maimum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing. Determine intervals of which the function is increasing or decreasing, determine relative etrema and zeros of the function with and without a graphing calculator. Determine if a relation is a function by the vertical line test. The function f given by f ( ) 4 is A. Increasing for, decreasing for, increasing for B. Decreasing for 0, increasing for 0 *C. Increasing for all D. Decreasing for all E. Decreasing for, increasing for, decreasing for Constant Decreasing Increasing Relative Maimum Relative Minimum Roots Solutions Vertical Line Test Zeros Students will get a graph and describe everything they know about that graph. Teachers will then lead the discussion on how to find specific values on the calculator. Section.5 P.() Functions. The student uses process standards in mathematics to eplore, describe, and analyze the attributes of The student makes connections between P.(F) graph eponential, power, trigonometric, in verse trigonometric, and functions, including step Recognize and graph the various parent functions: linear, quadratic, cubic, square root, rational, piecewise, absolute value, and greatest integer Recognize the equation of and graph the various parent functions Recognize f() = / (hyperbolic) Graph the piecewise function: f() 4, < = { +, < 0 +, 0 Absolute Value Func. Constant Function Cubic Function Greatest Integer Func. Linear Function Quadratic Function Rational Function Square Root Function Students will play a matching game. They will be given either the name of function, the graph of the function, or the equation of the function and their counterparts Section.6 LTF Pre-Cal Frantic Functions Last Edit 07-08 Page
P.() Functions. The student uses process standards in mathematics to eplore, describe, and analyze the attributes of The student makes connections between P.(A) use the composition of two functions to model and solve real-world problems. P.(B) demonstrate that function composition is not always commutative. P.(C) represent a given function as a composite function of two or more Perform function operations including composite functions and their domain. Students will demonstrate proficiency verbally, numerically, symbolically and graphically. If h is the function given by h( ) f ( g( )), where f ( ) g( ) A. and, then h ( ) B. C. D. E. Answer: E Composite Function Make function machines by giving each student a different function and a different operation or composite form. Section.8 Last Edit 07-08 Page 4
P.() Functions. The student uses process standards in mathematics to eplore, describe, and analyze the attributes of The student makes connections between P.(E) determine an inverse function, when it eists, for a given function over its domain or a subset of its domain and represent the inverse using multiple representations. Find and verify the inverse of Understand the definition and properties of inverse functions and be able to eplain it in words. Show that two functions are inverses by composition. If f( ), then the inverse function, given by A. B. C. D. E. Answer: C f ( ) f, is Horizontal Line Test Inverse Function One-to-one Function Find inverse functions algebraically and graph the inverse functions by looking at the symmetry about the line y=. Compare the two results using domain and range. Section.9 Last Edit 07-08 Page 5