Question

Compare the graph of the function with the graph of its parent function.

y = x - 6
a) y = x - 6 is f(x) = x shifted up 6 units.
b) y = x - 6 is f(x) = x shifted down 6 units.
c) y = x - 6 is f(x) = x horizontally stretched 6-fold.
d) y = √(x - 6) is f(x) = √x shifted to the left 6 units.

Answer 1

The graph of y = x - 6 is the same as the graph of y = x shifted down 6 units.

Step-by-step explanation:

The graph of the function y = x - 6 can be compared to the graph of its parent function, which is the line y = x.

When comparing the two graphs, we can see that the graph of y = x - 6 is the same as the graph of y = x shifted down 6 units. This means that all the points on the graph of y = x have been moved down 6 units to create the graph of y = x - 6.

Therefore, option b) y = x - 6 is f(x) = x shifted down 6 units is the correct comparison.