Question

The graph of f(x) was transformed to create the graph of g(x) = f(x + 5). What is the graph of G? Where would the two points be placed on a Coordinate grid to connect the line

Answer 1

g(x) = f(x + 5) is the graph of f shifted horizontally 5 units to the left.

How to place two points to draw the line:
- Take any two points on the original f: (x1, y1) and (x2, y2).
- For g, subtract 5 from each x-coordinate and keep the y the same:
g has points (x1 − 5, y1) and (x2 − 5, y2).
- Connect those two points (they have the same slope as the original line).

Example:
- If f passes through (0, 2) and (4, −1), then g will pass through (0 − 5, 2) = (−5, 2) and (4 − 5, −1) = (−1, −1). Draw the line through (−5, 2) and (−1, −1).