The function f(x) = -5x. The graph of g(x) is f(x) vertically compressed by a factor of 1/4 and reflected in the x axis. What is the function rule for g(x)?
g(x) = -20x
g(x) = -5/4x
g(x) = 20x
g(x) = 5/4x
I think it's B, but I'm really not sure... please help, thanks.
B does the compression, but not the reflection.
Reflection through the x-axis takes (x,y) -> (x,-y)
To find the function rule for g(x), which is the graph of f(x) vertically compressed by a factor of 1/4 and reflected in the x-axis, we need to perform two transformations on the original function f(x) = -5x.
First, let's consider the vertical compression. When a function is vertically compressed by a factor of k, where k is a positive number, the rule of the new function becomes f(x) = k * original function. In our case, the original function is -5x and the compression factor is 1/4. Therefore, the new rule after the vertical compression is g(x) = (1/4)(-5x).
Secondly, we have to reflect the vertically compressed function in the x-axis. When a function is reflected in the x-axis, the sign of the function's rule is negated. Thus, the new rule after reflecting in the x-axis is g(x) = -(1/4)(-5x).
Simplifying the equation, we get:
g(x) = (1/4)(-5x) = - (1/4)(5x) = -5/4x
So, the correct function rule for g(x) is g(x) = -5/4x, which corresponds to option B.