Ex: Express h(x) so that it represents the graph of f(x) = x2 – 3 reflected over the x-axis? y-axis?

Stretching & Shrinking Complete the exploration on p. 136 First 8 min. No talking Last 8 min. you can discuss with a neighbor

Stretches and Shrinks Let c be a positive real number. The following transformations result in stretches or shrinks of the graph of y = f(x). Horizontal stretches or shrinks y = f(x/c) a stretch by a factor of c if c > 1 a shrink by a factor of c if c < 1 Vertical stretches or shrinks y = cf(x) a stretch by a factor of c if c > 1

a) f(x) = |x + 2| b) f(x) = x2 + x - 2 Ex 3 Transform the given function by (a) a vertical stretch by a factor of 2 and (b) horizontal shrink by a factor of 1/3. a) f(x) = |x + 2| b) f(x) = x2 + x - 2

Combining Transformations The order in which transformations are performed often affect the graph that results Ex 4 Use f(x) = x2 to perform each transformation. Write the formula for the resulting function. A horizontal shift 2 units to the right, a vertical stretch by a factor of 3, and vertical translation 5 units up Apply the transformations in the reverse order Are the graphs the same? Are the formulas the same?

Tonight’s Assignment P. 140-141 Study for Unit #1B Test on Tuesday, Sept. 25th