Write the function rule g(x) after the given transformations of the graph of f(x)equals 4x.
reflection in the y-axis; vertical compression by a factor of one eighth
g(x)= ?
reflection: x → -x
compression: y → y/8
so that gives g(x) = f(-x)/8 =
Well, well, well! If we're reflecting in the y-axis, that means we're flipping the graph horizontally. So, we need to stick a negative sign in front of the x, giving us -x.
Now, for the vertical compression by a factor of one eighth, it means we're squeezing the graph vertically. To do that, we multiply the whole expression by 1/8.
So, drumroll please... Here's our final function rule for g(x):
g(x) = -x/8
To find the function rule for g(x) after the given transformations of the graph of f(x) = 4x (reflection in the y-axis and vertical compression by a factor of one eighth), we can apply each transformation one by one.
First, let's apply the reflection in the y-axis. A reflection in the y-axis can be achieved by negating the x-coordinate. So, we can change the sign of the x term in the function.
The function after the reflection is: f(x) = -4x.
Next, let's apply the vertical compression by a factor of one eighth. To compress a function vertically by a factor of one eighth, we need to multiply the function by 1/8.
The function after the vertical compression is: f(x) = (-4/8)x.
Simplifying further, we get: f(x) = -1/2x.
Therefore, the function rule for g(x) after the given transformations is:
g(x) = -1/2x.
To find the function rule for g(x) after the given transformations, we need to apply each transformation step by step.
1. Reflection in the y-axis:
When a function is reflected in the y-axis, we switch the sign of the x-values. In this case, the reflection does not affect the vertical compression, so we switch the sign before applying the vertical compression.
f(x) = 4x
After reflection, the x-values become -x:
f(-x) = 4(-x)
2. Vertical compression by a factor of one eighth:
To vertically compress a function, we multiply the function by a fraction less than 1. In this case, we compress the function by a factor of one eighth, which means multiplying it by 1/8.
f(-x) = 4(-x)
After vertical compression by 1/8:
g(x) = (1/8) * f(-x)
= (1/8) * 4(-x)
Simplifying, we get the final function rule for g(x):
g(x) = -1/2x