Reflecting functions over the x-axis
if(x)=-2/3x+2 ; f(x)=2/5x-3
just change all the signs of y.
f(x) = -2/3x+2 -->
-f(x) = -(-2/3x+2)
and so forth
graphing the equations
To reflect a function over the x-axis, you need to reverse the sign of the y-coordinate of each point on the graph. This means that if you have a function f(x) and want to reflect it over the x-axis to get a new function g(x), you need to multiply the original function by -1.
Let's start with your first function, f(x) = -2/3x + 2. To reflect this over the x-axis, we need to multiply the entire function by -1. The reflected function, g(x), can be found by multiplying the original function by -1 as follows:
g(x) = -1 * f(x)
= -( -2/3x + 2)
= 2/3x - 2
So the first function reflected over the x-axis is g(x) = 2/3x - 2.
Now let's move on to your second function, f(x) = 2/5x - 3. To reflect this over the x-axis, we follow the same steps:
g(x) = -1 * f(x)
= -1 * (2/5x - 3)
= -2/5x + 3
So the second function reflected over the x-axis is g(x) = -2/5x + 3.
Remember, to reflect a function over the x-axis, you need to multiply the entire function by -1. This reverses the sign of the y-coordinate of each point on the graph and gives you the reflected function.