Write the function rule g(x) after the given transformations of the graph of f(x)= -2x.
reflection in the x-axis;vertical compression by a factor of 1/4.
g(x) = ?
g(x) = x / 2
Well, well, well. Looks like we're going to have some fun with this! Let's break it down step by step, shall we?
First off, we're dealing with the function f(x) = -2x. So, if we want to reflect it in the x-axis, we just need to take the opposite of the function, like flipping a pancake. So, g(x) = -(-2x). Simplifying that gives us g(x) = 2x.
Now, we want to vertically compress the graph by a factor of 1/4. Think of it as squishing the function like a bug. To do this, we're going to multiply the function by 1/4. So, the final answer is g(x) = (1/4)(2x). Simplifying that gives us g(x) = 1/2x.
Ta-da! We've successfully reflected the graph in the x-axis and vertically compressed it. Now go out there and show off your squished, flipped function!
To create the function rule g(x) after the given transformations of the graph of f(x) = -2x, we need to follow these steps:
1. Start with the original function f(x) = -2x.
2. Apply a reflection in the x-axis. This means we change the sign of the original function. Therefore, the reflection of -2x is 2x.
3. Next, apply a vertical compression by a factor of 1/4. To compress the graph vertically, we need to multiply the function by the compression factor. Thus, multiplying 2x by 1/4 gives us g(x) = (1/4)(2x).
4. Simplify the expression. By multiplying 2x by 1/4, we get g(x) = (1/4)(2x) = (1/2)x.
Therefore, the function rule g(x) after the given transformations is g(x) = (1/2)x.
To determine the function rule g(x) after the given transformations, we need to apply each transformation to the original function, f(x) = -2x, one by one.
The first transformation is a reflection in the x-axis. This means that each point on the original graph will be reflected over the x-axis, resulting in a change in the sign of the y-coordinate.
So, after the reflection, the function becomes f(x) = -(-2x), which simplifies to f(x) = 2x.
The second transformation is a vertical compression by a factor of 1/4. This means that each point on the graph will be vertically compressed towards the x-axis by dividing the y-coordinate by 1/4 (which is the same as multiplying it by 4).
So, after the vertical compression, the function becomes f(x) = 4 * 2x, which simplifies to f(x) = 8x.
Therefore, the function rule g(x) after the given transformations of the graph f(x) = -2x (reflection in the x-axis; vertical compression by a factor of 1/4) is g(x) = 8x.