Final answer:
The function g(x) is the transformation of f(x) that includes a horizontal shift right by 4 units, a reflection across the x-axis, and a vertical shift upward by 5 units.
Step-by-step explanation:
The student has asked to describe the transformation of the function f(x) to the function g(x) = -f(x - 4) + 5. Looking at the new function g(x), we notice several transformations applied to f(x).
Firstly, the expression (x - 4) inside the function indicates a horizontal shift. According to algebraic rules, when we subtract a number from x in the function's argument, it translates the graph horizontally to the right by that number of units. In this case, f(x) is shifted 4 units to the right.
Secondly, the negative sign in front of the function f(x) implies a reflection across the x-axis. This is because applying a negative sign to a function’s output value reflects it over the x-axis, changing the sign of all the y-values of the original function.
Lastly, the addition of +5 at the end of the function indicates a vertical shift. Adding a number to the entire function translates the graph upwards by that number of units. Therefore, g(x) is shifted up 5 units.
Combining these transformations, g(x) is the result of translating f(x) to the right by 4 units, reflecting it across the x-axis, and then shifting it upward by 5 units.