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) = 3x-2
g(x) = -3x-2
g(x) = 3x+2
g(x) = -3x+2
I need an explanationf or this in order to find the correct answer by myself.
If it is vertically compressed by a factor of 1/4, then all the y values are 1/4 as big: g(x) = 1/4 f(x)
If it is reflected in the x-axis, all the y values change sign: g(x) = -f(x)
So, you want g(x) = -1/4 f(x) = -5/4 x
None of those choices looks any good. Do you have the right problem?
You can find explanations in your text, or online using google or youtube, searching for graphs transformations
Also explain it to where I can understand this question myself.
To vertically compress a function by a factor of 1/4, we multiply the entire function by 1/4. So, for the function f(x) = -5x, the vertically compressed function, let's call it g(x), will be g(x) = (1/4)*f(x).
Now, to reflect the function in the x-axis, we take the negative of the expression g(x). So, the function g(x) = -[(1/4)*f(x)] = -[(1/4)*(-5x)] = -(-5/4)x = (5/4)x.
Therefore, the function rule for g(x) is g(x) = (5/4)x.
To find the function rule for g(x) when it is vertically compressed by a factor of 1/4 and reflected in the x-axis, we need to understand the transformations applied to the original function f(x) = -5x.
1. Vertical compression by a factor of 1/4: This means that the original y-values will be multiplied by 1/4, causing the graph to become narrower. So, instead of -5x, we have -(1/4)(-5x) or (5/4)x.
2. Reflection in the x-axis: This means that all y-values will be multiplied by -1, causing the graph to be reflected below the x-axis. So, now we have -1(5/4)x or -5/4x.
Therefore, the function rule for g(x) is g(x) = -5/4x.
Now let's compare this with the given choices:
a) g(x) = 3x-2
b) g(x) = -3x-2
c) g(x) = 3x+2
d) g(x) = -3x+2
None of the given choices match the correct function rule of g(x) = -5/4x. So, none of the provided options is correct.