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)
this is for Families of Function test
1. C each output for y=x-3 is 3 less than the corresponding output for y=z. The graph of y=x-3 is the graph y=x translated down 3 unit
2. B y=1/2x
3. B g(x)=-3x-2
4. D g(x)=5/4x
5. D the graph of g(x) is the graph of f(x) translated to the left 7 units and up 9 unit
hope this helped y’all gn
Well, looks like g(x) is going through a bit of a transformation circus! To vertically compress f(x) by a factor of 1/4, we multiply the entire function by 1/4. And to reflect it in the x-axis, we put a negative sign in front of the function. So, let's get silly with it and determine the function rule for g(x):
g(x) = -1/4 * f(x)
So, putting g(x) = -1/4 * (-5x), we can simplify:
g(x) = 5/4 * x
Ta-da! The function rule for g(x) is g(x) = 5/4 * x. Enjoy the show!
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 apply these transformations to the original function f(x) = -5x.
First, let's consider the vertical compression by a factor of 1/4. This means that the vertical values of the graph will be multiplied by 1/4. Thus, the new function after the vertical compression is:
g₁(x) = (1/4) * f(x)
Next, we have to reflect the graph in the x-axis. This reflection is accomplished by changing the sign of the function's output. Therefore, the new function after the reflection is:
g(x) = -g₁(x) = -(1/4) * f(x)
Since the original function f(x) = -5x, we substitute this into the equation to get the final function rule for g(x):
g(x) = -(1/4) * (-5x) = (5/4)x
So, the function rule for g(x) is g(x) = (5/4)x.
To find the function rule for g(x), which is obtained by vertically compressing f(x) by a factor of 1/4 and reflecting it in the x-axis, you can follow these steps:
Step 1: Start with the original function f(x) = -5x.
Step 2: Apply the vertical compression by multiplying the expression -5x by 1/4, which gives us g(x) = (1/4)(-5x).
Step 3: Simplify the expression by applying the multiplication: g(x) = -5/4 * x.
Step 4: Finally, apply the reflection in the x-axis by multiplying the expression by -1, resulting in g(x) = (-1)(-5/4) * x.
Combining these steps, the function rule for g(x) is g(x) = 5/4 * x.
compress: f(x) -> 1/4 f(x)
reflect: f(x) -> -f(x)
g(x) = -1/4 f(x) = 5/4 x