Beginning Activity Beginning Activity 2: Verbal Descriptions of Functions
The outputs of most real functions we have studied in previous mathematics courses have been determined by mathematical expressions. In many cases, it is possible to use these expressions to give step-by-step verbal descriptions of how to compute the outputs. For example, if
we could describe how to compute the outputs as follows:
| Step | Verbal Description | Symbolic Result |
|---|---|---|
| 1 | Choose an input. | \(x\) |
| 2 | Multiply by 3. | \(3x\) |
| 3 | Add 2. | \(3x + 2\) |
| 4 | Cube the result. | \(( {3x + 2} )^3\) |
Complete step-by-step verbal descriptions for each of the following functions.
1.
\(f\x \mathbb{R} \to \mathbb{R}\) by \(f( x ) = \sqrt {3x^2 + 2}\text{,}\) for each \(x \in \R\text{.}\)
2.
\(g\x \mathbb{R} \to \mathbb{R}\) by \(g( x ) = \sin \! \left( {3x^2 + 2} \right)\text{,}\) for each \(x \in \R\text{.}\)
3.
\(h\x \mathbb{R} \to \mathbb{R}\) by \(h( x ) = e^{3x^2 + 2}\text{,}\) for each \(x \in \R\text{.}\)
4.
\(G\x \R \to \R\) by \(G(x) = \ln ( x^4 + 3 )\text{,}\) for each \(x \in \R\text{.}\)
5.
\(k \x \R \to \R\) by \(k(x) = \sqrt[3]{\dfrac{\sin (4x + 3)}{x^2 + 1}}\text{,}\) for each \(x \in \R\text{.}\)