if a function f(x) us shifted to the left one unit what function represents the transformation
f(x+1)
f(x-1)
f(x)+1
f(x)-1
The correct function that represents the transformation of shifting f(x) to the left one unit is f(x+1).
When a function is shifted to the left one unit, the function that represents this transformation is f(x+1).
When you shift a function to the left by one unit, it means that each point on the graph of the function moves one unit to the left. This lateral shift affects the x-coordinates of the points on the graph.
To represent this transformation, we can use the function notation. The original function is denoted as f(x), and to shift it one unit to the left, we need to adjust the x-coordinate within the function. There are two common ways to achieve this:
1. f(x+1): In this case, we add 1 to the x-coordinate inside the function. This results in the entire graph shifting to the left by one unit. For example, if the original graph had a point (2, 3), after the transformation, it would become (1, 3), as the x-coordinate is reduced by 1.
2. f(x-1): In this case, we subtract 1 from the x-coordinate inside the function. Similar to the first option, this will shift the entire graph one unit to the left. Using the same example, the point (2, 3) in the original graph would become (3, 3) after the transformation, as the x-coordinate is increased by 1.
In summary, when a function f(x) is shifted to the left by one unit, the function representations for the transformation are f(x+1) and f(x-1). The choice between them depends on whether you want to express the shift as addition or subtraction in the function notation.