Question

Which of the following statements best describes the effect of replacing the graph of y = f(x) with the graph of y = f(x + 6)? The graph of y = f(x) will shift up 6 units. The graph of y = f(x) will shift down 6 units. The graph of y = f(x) will shift left 6 units. The graph of y = f(x) will shift right 6 units.

Answer 1

Answer:

The graph of y = f(x) will shift right 6 units.

Step-by-step explanation:

Have the same test and if a positive number gets added to the x value then it goes right and vice versa for negatives

Answer 2

Answer:

The graph of y = f(x) will shift left 6 units, as shown in figure a.

Step-by-step explanation:

A translation means we are able to move the graph of a function up or down - normally called Vertical Translation -  and right or left - commonly called Horizontal Translation.

If we replace the graph of y = f(x) with the graph of y = f(x + 6). It means we have added 6 units to the input, meaning the graph y = f(x) will shift left by 6 units as 6 is being added directly to the  x, so it is f(x + 6).

For example, if y = x² is the original function and of 6 is directly added to x i.e. f(x + 6), making it y = (x + 6)². So, we can easily observe that there will be a horizontal translation left of 8 units, as shown in figure a.

So, the graph of y = f(x) will shift left 6 units.

Keywords: graph shift, translation

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