The function f(x)=−2x+1 is linear. Select the function g(x) based on the rule rx−axis.(1 point)

Question

Responses

g(x)=2x−1
g left parenthesis x right parenthesis equals 2 x minus 1

g(x)=−2x−1
g left parenthesis x right parenthesis equals negative 2 x minus 1

g(x)=2x+1
g left parenthesis x right parenthesis equals 2 x plus 1

g(x)=−(2x−1)
g left parenthesis x right parenthesis equals negative left parenthesis 2 x minus 1 right parenthesis

Answer 1

To find the function \( g(x) \) based on the rule "reflect across the x-axis" from the function \( f(x) = -2x + 1 \), we take the function \( f(x) \) and multiply it by -1.

Reflecting the function across the x-axis means that:

\[ g(x) = -f(x) \]

So we calculate:

\[ g(x) = -(-2x + 1) = 2x - 1 \]

Now, let's look at the provided options:

1. \( g(x) = 2x - 1 \)
2. \( g(x) = -2x - 1 \)
3. \( g(x) = 2x + 1 \)
4. \( g(x) = - (2x - 1) \)

The correct function after reflecting \( f(x) = -2x + 1 \) across the x-axis is \( g(x) = 2x - 1 \).

Therefore, the answer is:

g(x) = 2x - 1.