Effect of the graph f(1/2x)
The graph of f(1/2x) would effectively stretch the x-axis by a factor of 2. This means that every point on the graph would be shifted horizontally by a factor of 2.
For example, if the point (2, 4) is on the original graph of f(x), then the point (1, 4) would be on the graph of f(1/2x). Similarly, if the point (-2, 2) is on the original graph of f(x), then the point (-1, 2) would be on the graph of f(1/2x).
This stretching of the x-axis would make the graph appear narrower compared to the original graph of f(x). The y-values of the graph would remain the same, as changing the x-values does not affect the y-values.
To determine the effect of the graph of f(1/2x), we can apply a series of transformations to the original function f(x).
1. Horizontal Stretch: The coefficient 1/2 in front of x implies that the graph will be horizontally stretched by a factor of 2 compared to the original function.
2. Vertical Stretch/Compression: Since there is no coefficient attached to f(x), there is no vertical stretch or compression. The y-values remain the same.
3. Horizontal Translation: The graph is translated horizontally by multiplying the x-values by 1/2. This means that every x-coordinate is halved compared to the original function.
Overall, the graph of f(1/2x) will be a horizontally stretched and horizontally translated version of the original graph f(x).
To understand the effect of the function f(1/2x), let's break it down step by step:
1. Scaling: The first thing to notice is the scaling factor of 1/2 in front of the x. This means that every x-coordinate on the graph is halved. So, if you had a point at x = 2, it would be scaled down to x = 1 when you apply the function f(1/2x).
2. Vertical Compression: Secondly, this function does not have any y-values or coefficients applied to it. This means that there is no vertical compression or expansion happening. The y-axis remains the same.
Putting it all together, the effect of the graph f(1/2x) is a horizontal scaling where every x-coordinate is halved. This means that the graph will become narrower or more compressed horizontally.
For example, let's consider the graph of the function f(x) = x^2. If we apply the function f(1/2x) to it, the x-values will be halved. So, the resulting graph will be f(1/2x) = ((1/2x)^2) = 1/4x^2. This means that the graph will be four times narrower or compressed horizontally compared to the original graph f(x) = x^2.