Write the function rule g(x) after the given transformations of the graph of f(x)=6x.
reflection in the y-axis; vertical compression by a factor of one third
g(x)= ?
g(x) = 1/3 f(-x) = -2x
Thank you, sir
To find the function rule g(x) after the given transformations, we'll apply each transformation one by one.
1. Reflection in the y-axis:
When a graph is reflected in the y-axis, the x-coordinate of each point is negated. In terms of the function rule, this is equivalent to multiplying the original function by -1.
So, after reflecting f(x)=6x in the y-axis, we have: f(x) = -6x.
2. Vertical compression by a factor of one third:
Vertical compression involves compressing or shrinking the graph vertically. To compress a graph vertically by a factor of one third, we multiply the function by the reciprocal of the compression factor, which in this case is 1/3.
So, after compressing f(x) = -6x vertically by a factor of one third, we have: g(x) = (-6x) * (1/3).
Simplifying g(x), we get: g(x) = -2x.
Therefore, the function rule g(x) after the given transformations is g(x) = -2x.
To find the function rule g(x) after the given transformations of the graph of f(x), you need to apply each transformation step by step.
First, let's start with the original function f(x) = 6x.
Step 1: Reflection in the y-axis
To reflect a function in the y-axis, we simply change the sign of the x-coefficient. Since the original function has a coefficient of 6 for x, the reflection in the y-axis would have a coefficient of -6. Therefore, the function after the reflection would be -6x.
f(x) (original) = 6x
After reflection: -6x
Step 2: Vertical compression by a factor of one third
To vertically compress a function, we multiply the entire function by the compression factor. In this case, the compression factor is one third (or 1/3). So we multiply the function obtained from the reflection (-6x) by 1/3.
-6x * (1/3) = -2x
Therefore, the function after the reflection and vertical compression is g(x) = -2x.