1.6 Reflections, Absolute Value and other transformations

1.6 Reflections, Absolute Value and other transformations Lesson Obj: Iwbat to take a given function and transform it by a given condition

Reflections Reflection over the x-axis is caused by changing to Reflection over the y-axis is caused by changing to

Reflection of a function • For for Reflect over the x-axis Reflect over the y-axis

Absolute Value functions… • Graph • Now graph

Absolute value over x-axis • To take absolute value of a function over the x-axis for negative values of x • For positive values of x • When you break up a function (positive and negative values), this is called a piecewise fcn.

Absolute value general form… Reflect across x-axis (vertically) Reflect across y-axis Does 3 things Leaves positive x’s alone Reflects the positive values for x from the negative Eliminates negative values for x • Does 2 things • Reflects negative values of x across the x-axis • Leaves positive values alone

Even and Odd functions Even function is when a function is reflected exactly across the y-axis For even fcn’s= • Even functions have even exponents within them and have the same outputs for x and –x. • Ex.

Odd functions • For odd fcn’s • Reflection across the x-axis and y-axis give the same result • Symmetric about the origin (0,0)

Example… • Reflect about the y-axis and then about the x-axis • Y-axis = horizontal dilation of (-1) • X-axis = opposite of f(x) • Graph all of the above

Assignment • Pg. 47 1, 2 • HW: 2-10 evens (in quick review) • Day 2 • Even and Odd fcn worksheet

1.6 Reflections, Absolute Value and other transformations