Final answer:
The transformation from f(x) = x to g(x) = x - 3 is a horizontal shift 3 units to the left, changing its y-intercept to -3 while retaining the same slope.
Step-by-step explanation:
The transformation from the graph of f(x) = x to the graph of g(x) = x − 3 can be described as a horizontal shift to the left by 3 units. This type of transformation is known as a translation. In the case of a linear function such as f(x) = x, which has a slope of 1 and passes through the origin, shifting it horizontally does not change the slope but changes the y-intercept.
The new function g(x) will still be a straight line with the same slope (a rise of 1 on the vertical axis for every increase of 1 on the horizontal axis), but it will intersect the y-axis at -3 instead of at the origin (0,0).
The transformation from the graph of f(x) = x^8 to the graph of g(x) = x - 3 can be described as a vertical translation downward by 3 units.
When we subtract 3 from the original function, the y-values of all the points on the graph decrease by 3. This means that every point on the graph of f(x) is moved downwards by 3 units to produce the graph of g(x).