Reflecting ordered pairs over the x- or y- axis
- to reflect over the x-axis: change sign of the y-coordinate
- to reflect over the y-axis: change sign of the x-coordinate
Reflecting a graph over the x-axis
To reflect an equation over the x-axis, make the x values opposite outside of the symbol. Examine what happens to make the parent graphs reflect over the x-axis:
Try reflecting the the absolute value function y = Ix+3I over the x-axis. We can tell from the table above that the function is translated to the left. To reflect the absolute value function over the x-axis, we simply put a negative sign before the symbol (in this case the absolute value bars). Our new equation would be: y = -Ix+3I. Check the graphs in your calculator, they should look like a mirror image of each other, reflected over the x-axis.
Now try reflecting reciprocal y = 1/x -4. The graph is translated down. To reflect this graph over the x-axis, we can put a negative sign in front of the 1:
y = -1/x -4
- linear: y = -x
- absolute value: y = -IxI
- square root: y = -SQRTx
- cubic: y = -x³
- parabola: y = -x²
- reciprocal: y = -1/x
Try reflecting the the absolute value function y = Ix+3I over the x-axis. We can tell from the table above that the function is translated to the left. To reflect the absolute value function over the x-axis, we simply put a negative sign before the symbol (in this case the absolute value bars). Our new equation would be: y = -Ix+3I. Check the graphs in your calculator, they should look like a mirror image of each other, reflected over the x-axis.
Now try reflecting reciprocal y = 1/x -4. The graph is translated down. To reflect this graph over the x-axis, we can put a negative sign in front of the 1:
y = -1/x -4
Reflecting a graph over the y-axis
To reflect an equation over the y-axis, make the x values opposite outside of the symbol. Examine what happens to make the parent graphs reflect over the y-axis:
- linear: y = -x
- absolute value: y = I-xI
- square root: y = SQRT(-x)
- cubic: y = -x³
- parabola: y = -x²
- reciprocal: y = -1/x