Mathematics | Course : Model Mathematics III (Integrated Pathway)
Domain - Building Functions
Cluster - Build new functions from existing functions.
[MIII.F-BF.B.3] - Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Include simple rational, radical, logarithmic, and trigonometric functions. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
- Expression
A mathematical phrase that combines operations, numbers, and/or variables (e.g., 32 ÷ a). - Function
A mathematical relation for which each element of the domain corresponds to exactly one element of the range. - Logarithmic function
Any function in which an independent variable appears in the form of a logarithm; they are the inverse functions of exponential functions. - Trigonometric function
A function (as the sine, cosine, tangent, cotangent, secant, or cosecant) of an arc or angle most simply expressed in terms of the ratios of pairs of sides of a right-angled triangle.
[MII.F-IF.C.7.a] -
Graph quadratic functions and show intercepts, maxima, and minima.*
[MIII.F-IF.C.7.b] -
Graph square root and cube root functions.*
[MIII.F-IF.C.7.c] -
Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.*
[PC.F-IF.C.7.d] -
(+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.*