Describe how the function g(x)=1/2|x-4| transforms the function f(x)=|x-4|
The graph of g(x) is the parent function f(x) vertically compressed by a factor of 2
The graph of g(x) is the parent function f(x) vertically stretched by a factor of 2
The graph of g(x) is the parent function f(x) horizontally stretched by a factor of 2
The graph of g(x) is the parent function f(x) horizontally compressed by a factor of 2
The correct answer is: The graph of g(x) is the parent function f(x) vertically compressed by a factor of 2.
The correct answer is: The graph of g(x) is the parent function f(x) vertically compressed by a factor of 2.
To describe how the function g(x) = 1/2|x-4| transforms the function f(x) = |x-4|, we can break it down into two parts: the coefficient of 1/2 and the absolute value function.
First, let's look at the coefficient of 1/2. This coefficient will affect the vertical scaling of the graph. When this coefficient is less than 1, it compresses the graph vertically, making it narrower. In this case, since the coefficient is 1/2, the graph of g(x) is vertically compressed by a factor of 2 compared to f(x). This means that every point on the graph of g(x) is only half the distance away from the x-axis compared to the corresponding point on the graph of f(x).
Next, let's consider the absolute value function. The absolute value function |x-4| reflects any negative values of (x-4) to their positive counterparts. In other words, it "flips" the part of the graph that lies below the x-axis to be above the x-axis. Both f(x) and g(x) have the same absolute value function |x-4|, so the reflection remains the same. Therefore, the transformation does not affect the horizontal position of the graph.
Putting these two parts together, the graph of g(x) = 1/2|x-4| can be described as the parent function f(x) = |x-4| vertically compressed by a factor of 2.