The function f(x)=−2x+1 is linear. Select the function g(x) based on the rule rx−axis.
The function g(x) based on the rule rx-axis would be g(x) = -1. This function reflects the graph of f(x) over the x-axis.
options are
g(x)=2x+1
g(x)=2x−1
g(x)=−2x−1
g(x)=−(2x−1)
The function g(x) based on the rule rx-axis would be g(x) = -(2x - 1). This function reflects the graph of f(x) over the x-axis.
The function that represents the reflection of f(x) across the x-axis is g(x) = -f(x).
Since f(x) = -2x + 1, we can substitute this expression to find g(x):
g(x) = -(-2x + 1)
= 2x - 1
Therefore, the function g(x) based on the rule of reflection across the x-axis is g(x) = 2x - 1.
To find the function g(x) based on the rule "rx-axis," we need to understand what the rule implies. The "rx-axis" means that we need to reflect the function about the x-axis.
Starting with the function f(x) = -2x + 1, to reflect it about the x-axis, we change the sign of the coefficient of x.
So, g(x) = -f(x) = -(-2x + 1) = 2x - 1.
Therefore, the function g(x) based on the rule "rx-axis" is g(x) = 2x - 1.