The parent function for g(x) = x + 2 is the identity function, f(x) = x, which is a straight line passing through the origin with a slope of 1.
To graph g(x) = x + 2, we start with the parent function and apply the transformation. The transformation for g(x) involves shifting the graph vertically upward by 2 units.
Here's the step-by-step process to graph g(x):
Plot points on the parent function, f(x) = x. For example, if x = -2, f(x) = -2; if x = 0, f(x) = 0; if x = 2, f(x) = 2.
Apply the vertical shift by adding 2 units to the y-coordinate of each point. For example, if the point on the parent function is (x, y), the corresponding point on g(x) will be (x, y + 2).
Connect the points to form a straight line. Since g(x) = x + 2 is a linear function, the graph will be a straight line with the same slope as the parent function.
The transformation of the parent function f(x) = x to g(x) = x + 2 results in a vertical shift upward by 2 units. This means that the graph of g(x) is the same as the parent function, but it is shifted upward by 2 units along the y-axis.
Visually, the graph of g(x) will be parallel to the parent function f(x), but it will be shifted upward by 2 units. The slope of the line remains the same, indicating that the transformation does not affect the steepness of the line.