Reflections
Key points
- Reflections of graphs consist of multiple points along the graph being reflected over a line.7
- Usually the x or y axis.
- Multiplying a function by -1, or using a negative coefficient, reflects a line over the x-axis.
- Replacing x with -x in a function reflects the line over the y-axis.
Reflecting a graph over the x-axis, or reflecting it vertically, can be done by putting using negative coefficients in front of it.
- When taking a pre-existing function, multiply it by -1 to find the resultant function reflected over the x-axis.
- Distribute this negative over each term in the function.
- y=3x^2-3x-3 reflected over the x-axis becomes y=-3x^2+3x+3, as each sign is changed.
- Distribute this negative over each term in the function.
- y=-f(x) is a reflection in the x-axis of y=f(x).
- A point (x,y) becomes (x,-y).
Reflecting a graph over the y-axis, or reflecting it vertically, can be done by replacing x with -x.
- y=3x^2-3x-3 reflected over the y-axis becomes y=3(-x)^2-3(-x)-3, as x is replaced with (-x).
- y=-f(x) is a reflection in the x-axis of y=f(x).
- A point (x,y) becomes (-x,y).
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