Question

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

a. g (x) = - (2x - 1)
b. g (x) = 2x - 1
c. g (x) = -2x - 1
d. g (x) = 2x + 1

Answer 1

To apply the rule for reflecting a function across the x-axis, you need to negate the entire function. This means that if a function is given as \( f(x) \), then its reflection \( g(x) \) will be defined by:

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

Given the function \( f(x) = -2x + 1 \), we can calculate the reflection across the x-axis:

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

Now, let's match this with the provided options:

a. \( g(x) = - (2x - 1) \)

b. \( g(x) = 2x - 1 \)

c. \( g(x) = -2x - 1 \)

d. \( g(x) = 2x + 1 \)

The correct choice is:

**b. \( g(x) = 2x - 1 \)**.