2.7

Topic

Composition of Functions

Practice by unit: Exponential and Logarithmic Functions

Sub-standards

• 2.7.B.1 — Construct a representation of the composition of two or more functions. Function composition is useful for relating two quantities that are not directly related by an existing formula.
• 2.7.B.2 — When analytic representations of the functions f and g are available, an analytic representation of f g( (x)) can be constructed by substituting g (x) for every instance of x in f .
• 2.7.B.3 — A numerical or graphical representation of f g ○ can often be constructed by calculating or estimating values for (x f , ( g x( ))).
• 2.7.C.1 — Rewrite a given function as a composition of two or more functions. Functions given analytically can often be decomposed into less complicated functions. When properly decomposed, the variable in one function should replace each instance of the function with which it was composed.
• 2.7.C.2 — An additive transformation of a function, f , that results in vertical and horizontal translations can be understood as the composition of g (x x ) = + k with f .
• 2.7.C.3 — A multiplicative transformation of a function, f , that results in vertical and horizontal dilations can be understood as the composition of g (x) = kx with f . UNIT 2