How does F(x+c) affect the graph of F(x)?

When considering how the expression F(x + c) affects the graph of F(x), it is important to understand the concept of horizontal shifting in function transformations.

For the function F(x + c), the graph of the original function F(x) is shifted horizontally. Specifically, the term (x + c) indicates that every point on the graph of F(x) moves to the left by c units. This type of transformation is a standard feature in function analysis, where adding a constant inside the function's argument results in a shift opposite to the direction of the sign of that constant. Hence, when c is positive, the shift is to the left, while if c were negative, it would shift to the right—confirming the horizontal nature of the transformation.

This principle extends from the way functions behave in response to their inputs. It does not affect the vertical position or stretch of the graph, nor does it create any reflection across an axis. Therefore, F(x + c) reflects how changes within the input to a function directly influence its position along the x-axis, affirming that the correct interpretation of this transformation is indeed a horizontal shift against the sign.