Bell Assignment 1.Graph the equation y = x 3 + 3x 2 – 1 on your GUT. Then use the graph to describe the increasing or decreasing behavior of the function. 2.Graph the following equation. f(x) = -½x – 6 ; x ≤ -4 x + 5 ; x > -4

1.4 Shifting, Reflecting, and Stretching Graphs

Ways to write functions: In Algebra 2: y = x y = (x+3) 2 y = 3x 2 In Pre-Cal h(x) = f(x) + 3 g(x) = f(x + 3) q(x) = 3 f(x) y = x 2 Original Function f(x) = x 2

Ways to write functions: In Algebra 2: y = x – 2 y = x -2 y = ½ x In Pre – Cal h(x) = f(x) – 2 p(x) = f(x – 2) q(x) = ½ f(x) y = x f(x)= x

Shifting and Reflecting Graphs Label Points: Notice (x, y)  (-x, y) Over _____ (x, y)  (x, -y) Over _____ y axis x axis so f(-x) reflects over the y axis because you negate the x value. - f(x) reflects over the x axis because you negate the y value.

f(-x) means to negate the x value and therefore reflects over the y axis. -f(x) means to negate the y value and therefore reflects over the x axis.

Compare the graph of each function with the graph of f(x) = x 3 In Words:In Terms of f(x) g(x) = x 3 – 1 Moves down 1 Unit g(x) = f(x) – 1 p(x) = 4x 3 Narrowerp(x) = 4f(x) h(x) = (x -1) 3 Moves to the right 1 unith(x) = f(x – 1) k(x) = (x + 2) 3 + 1Moves left 2 units and 1 unit upk(x) = f(x + 2) + 1

Find an equation for each shift of f(x) = x 2 g(x) = f(x) + 2 g(x) = x h(x) = f(x+3) h(x) = (x + 3) 2 p(x) = f(x – 4) + 2 p(x) = (x – 4) 2 + 2

Reflections: h(x) = -f(x) means reflect over the x axis… why? h(x) = f(-x) means reflect over the y axis…why? f(x) = x 4 Original Graph In terms of f(x) In terms of x In terms of f(x) In terms of x g(x) = -f(x) + 3 g(x) = -x h(x) = -f(x – 4) h(x) = - (x – 4) 4

Order is Important when Graphing!!! R x SR y (reflect over x-axis, shift, reflect over y-axis)

Graph. y = √(2-x) + 3 y = √(-x+2) + 3 Then Graph Rewrite.

Graph. y = -1(x – 3) 3 – 4

Graph. y = -(x+2) 3 + 4

Graph. y = (2-x) 3 + 4

Consider the following graph. (a)y = f(x) -1 (b)y = f(x+1) (c)y = f(x-1) (d)y = -f(x-2) (e)y = f(-x) (f)y = ½f(x) (g)y = f(2x)

Exit Pass Describe the sequence of events. The original graph is f(x) = x 3 1.g(x) = -f(x+3) – 2 2.h(x) = f(4-x) 3.p(x) = f(x-1)-3