Lesson 4-3Lesson 4-3Reflecting Graphs:Reflecting Graphs:

SymmetrySymmetry

Use your grapher to sketch the following:

Use your grapher to sketch the following:

Use your grapher to sketch the following:

Use your grapher to sketch the following:

Use your grapher to sketch the following:

Use your grapher to sketch the following:

Use your grapher to sketch the following:

Use your grapher to sketch the following:

Use your grapher to sketch the following:

Use your grapher to sketch the following:

Use your grapher to sketch the following:

Use your grapher to sketch the following:

Use your grapher to sketch the following:

Use your grapher to sketch the following:

Use your grapher to sketch the following:

Use your grapher to sketch the following:

Use your grapher to sketch the following:

Reflections over the x-axis:

Reflections over the x-axis:

• A graph is a reflection over the x-axis if all (x, y) can be paired to (x, -y).

Reflections over the y-axis:

Reflections over the y-axis:

• A graph is a reflection over the y-axis if all (x, y) can be paired to (-x, y).

Reflections over the line y = x:

Reflections over the line y = x:

• A graph is a reflection over the line y = x if all (x, y) can be paired to (y, x).

Reflections over the origin:

Reflections over the origin:

• A graph is a reflection in the origin if all (x, y) can be paired to (-x, -y).

Use symmetry to sketch the graph of:

Use symmetry to sketch the graph of:

Think: Could you graph y = x4 ?

Use symmetry to sketch the graph of:

Think: Could you graph y = x4 ?

So, first trade places with x and y then solve for y.

Use symmetry to sketch the graph of:

x4 = y + 1, solve for y

Use symmetry to sketch the graph of:

x4 = y + 1, solve for y

x4 – 1 = y

Use symmetry to sketch the graph of:

Graph and then let every (x, y) become (y, x).

Use symmetry to sketch the graph of:

Graph and then let every (x, y) become (y, x).

Line of symmetry:

Line of symmetry:

• A line that is the perpendicular bisector of any segment joining any pair of corresponding points.

Point of symmetry:

Point of symmetry:

• A point 0 such that it is possible to pair the points of the graph in such a way that 0 is the midpoint of the segment joining each pair.

For quadratics:

For quadratics:

• Axis of symmetry -

For cubics:

For cubics:

• Point of symmetry -

Assignment:

Pgs. 135-137C.E. 1-8 all,

W.E. 1-19 odd