Question

Find g(x), where g(x) is the reflection across the x-axis of f(x)=4x+10

Answer 1

To find the reflection of a function across the x-axis, we simply need to change the sign of the y-coordinates of the function's points. Therefore, the reflection of f(x) = 4x + 10 across the x-axis is g(x) = -(4x + 10) = -4x - 10.

Explanation:

To find the reflection of a function across the x-axis, we can follow these steps:

1. Start with the equation of the original function, which in this case is f(x) = 4x + 10.
2. Change the sign of the y-coordinates of the function's points. This means that we need to multiply the entire equation by -1.
3. Substitute the result from step 2 into the original equation to find the reflected function. In this case, we get g(x) = (-1)(4x + 10) = -4x - 10.

Here is an example of how this works in practice. Let's say that the original function f(x) has the points (1,14) and (2,18).

The reflection of these points across the x-axis would be (1,-14) and (2,-18), respectively.

To find the equation of the reflected function g(x), we would simply substitute these points into the equation from step 3 to get g(x) = -4x - 10.