What happens when you change the graph of f(x)
to f(−x)
?(1 point)
Responses
The graph is reflected across the y-axis.
The graph is reflected across the y-axis.
The line is reflected across the x-axis.
The line is reflected across the x-axis.
The graph is moved 1 unit to the left.
The graph is moved 1 unit to the left.
The graph is moved 1 unit down.
The line is reflected across the y-axis.
The graph is reflected across the y-axis.
The correct answer is "The graph is reflected across the y-axis.".
To understand why this is the case, you need to understand the effect of replacing x with -x in a function. In this case, you are given a function f(x) and asked what happens when you replace x with -x, resulting in f(-x).
If a point (x, y) lies on the graph of f(x), then replacing x with -x would give us (-x, y). This means that the point (-x, y) would lie on the graph of f(-x).
Now, let's consider the effect of this replacement on the graph itself. When we replace x with -x, we are essentially reflecting the x-values across the y-axis. In other words, each point on the original graph that had an x-coordinate of x would now have an x-coordinate of -x. This reflects the graph across the y-axis.
So, the correct answer is that the graph is reflected across the y-axis.