how do i reflect when x is greater than 1

Answer 1

Hi Axel,

First, let us clarify how reflections change the coordinates of a point.

When reflecting a point over the y-axis, the new x value takes on the opposite sign. For example, a point in quadrant 2 has a positive y value and a negative x value. If that point is reflected over the y-axis, it now sits in the 1st quadrant with a positive y value and a positive x value. The negative x became a positive x.

This means that when you reflect over the y axis, for any x in the function f(x), we put in -x instead to get f(-x)

When reflecting a point over the x-axis, the new y value takes on the opposite sign. For example, if you have a point in quadrant 3, both the x and y values will be negative. After a reflection over the x-axis, the point will now sit in the 2nd quadrant where the x value is negative and the y value is positive. The negative y became a positive y.

This means that when you reflect over the x-axis, the y value, or the output of the function f(x), takes on the negative value. This gives us the function -f(x)

If you have an inequality, such as x > 5, it would mean that all values to the right of (greater than) the line x = 5 are included in the answer. This is usually represented by shading in the included area.

To reflect over the y axis, we use the equation f(-x)

If f(x) = x > 5

Then f(-x) = -x > 5

then we can multiply by -1 on both sides to get,

f(-x) = x < -5

Remember that when we multiply an inequality by a negative, the direction of the inequality flips.

So, after reflecting x > 5 over the y axis, we get the equation x < -5.

This new equation includes all values less than, or to the left of, but not including, the line x = -5

I hope that helps!