Final answer:
Examples of functions with an absolute value expression and a vertex of (-1,3) are f(x) = 2| x + 1 | + 3 and g(x) = -3| x + 1 | + 3, where the coefficients 2 and -3 indicate the steepness and orientation of the graph respectively.
Step-by-step explanation:
To provide two examples of functions involving an absolute value expression and having a vertex at (-1,3), let's start with the vertex form of an absolute value function, which is y = a| x - h | + k, where (h, k) is the vertex of the function.
Since we want the vertex to be at (-1,3), we substitute h = -1 and k = 3. Example functions could be:
- f(x) = 2| x + 1 | + 3
- g(x) = -3| x + 1 | + 3
For f(x), the vertex is (-1,3), and the number 2 indicates how steep the 'V' shape of the graph is. For g(x), the vertex remains the same, but due to the negative coefficient -3, the 'V' shape is inverted and steeper.