Final answer:
The function f(x) = -2x + 1 translated by -x results in its graph being shifted 1 unit to the right, calculated by the transformation formula f(x + 1). A function transformation either "moves" or "resizes" or "reflects" the graph of the parent function. There are mainly three types of function.
Step-by-step explanation:
The student is asking about translation of the function f(x) = -2x + 1 by -x. In the context of algebra and function translation, f(x - d) translates the function in the positive x-direction by a distance d, and f(x + d) translates it in the negative x-direction by the same distance. To apply this to the given function f(x), and determine the translation of the point (3,-5), the transformation formula applied will be f(x - (-1)) or f(x + 1). Thus, translating the function by -x is the same as shifting it 1 unit to the right along the x-axis.
A translation occurs when every point on a graph (representing a function) moves by the same amount in the same direction. There are two types of translations of functions. Horizontal Translation of Functions: In this translation, the function moves to the left side or right side.
Transformation of functions means that the curve representing the graph either "moves to left/right/up/down" or "it expands or compresses" or "it reflects". For example, the graph of the function f(x) = x2 + 3 is obtained by just moving the graph of g(x) = x2 by 3 units up. Function transformations are very helpful in graphing the functions just by moving/expanding/compressing/reflecting the curve without actually needing to graph it from scratch.