Practice Function as Mapping in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Viewing a function as a mapping means thinking of it as an explicit association from each element of the domain to exactly one element of the codomain.
Like a dictionary: every word maps to a definition. Every input maps to an output.
Example 1
easyLet f: \{1,2,3\} \to \{a,b,c\} be defined by f(1)=a, f(2)=a, f(3)=c. Determine whether f is a valid function, and find its range.
Example 2
mediumExplain why the relation R = \{(1,2),(1,3),(2,5)\} is NOT a function from \{1,2\} to \{2,3,5\}.
Example 3
easyWhich of the following sets of ordered pairs defines a function from \{1,2,3\} to \mathbb{R}? (A) \{(1,5),(2,5),(3,5)\} (B) \{(1,2),(2,3)\} (C) \{(1,0),(2,1),(3,2),(1,4)\}
Example 4
mediumLet f: \mathbb{R} \to \mathbb{R}, f(x) = x^2. Find f^{-1}(\{4\}) (the pre-image of 4) and explain why f does not have an inverse function on all of \mathbb{R}.