Practice Problems for 1/13
- For a function \(f:A \rightarrow B\), \(A\) is called the domain and \(B\) is called the co-domain.
- True or False: The range of a function must be equal to its co-domain. (Write one sentence justifying your response.)
- True or False: The map \(f: \mathbb{R}\rightarrow \mathbb{R}\) by \(f(x)=x^2-1\) is a function. (Write one sentence justifying your response.)
- True or False: The map \(f: \mathbb{R}\rightarrow [0,\infty)\) by \(f(x)=x^2-1\) is a function. (Write one sentence justifying your response.)
Note: \(\mathbb{R}\) denotes the set of all real numbers.
- Write a step by step procedure for how one could check whether or not a function \(f\) is an odd function.
Is it possible for a function to be both even and odd? Explain.
- Suppose you would like to graph both \(f(x)=x^3\) and \(g(x)=\frac{1}{2}(4x)^3-1\). Make a bullet point list of each change (i.e. vertical/horizontal shifts and/or scales) you would need to carry out to get from \(f\) to \(g\).