Mathematics

Mathematics

Problem

Consider the following four real-valued functions: (a) f1(x)=5f_{1}(x)=5, (b) f2(x)=x3−4xf_{2}(x)=x^{3}-4x, (c) f3(x)=1xf_{3}(x)=\dfrac{1}{x}, x≠0x\neq0, (d) f4(x)=∣x+1∣f_{4}(x)=|x+1|. Answer the questions that follow. a. (i) For each function, identify the parent family to which it belongs and write one key algebraic or graphical property that supports your identification. b. (ii) For each function, state its domain and range, giving justification in each case.

Browse the problem library