FST Quick Check Up Sketch an example of each function: Identity Function Absolute Value Function Square Root Function Quadratic Function Cubic Function Reciprocal Function p.1 FST Quick Check Up Sketch an example of each function: Identity Function Absolute Value Function Square Root Function Quadratic Function Cubic Function Reciprocal Function

Discuss the domain, range, symmetry, intercepts, extrema & continuity of each: Identity Function Absolute Value Function Square Root Function Quadratic Function Cubic Function Reciprocal Function Discuss the domain, range, symmetry, intercepts, extrema & continuity of each: Identity Function Absolute Value Function Square Root Function Quadratic Function Cubic Function Reciprocal Function

Description Vertical shift c units upward Horizontal shift c units to the right Reflection over the y-axis Vertical shrink by a factor of c Horizontal stretch by a factor of c Transformation (x, cy) where c > 1 (cx, y) where c > 1 Function Notation y =f (cx) (x, y - c) y =f (x + c) (x,- y) 1a. Complete the table 2b. Give a transformation which would make f(x) a graph of an odd function 2a.

3b. Which functions are even? 3a. 4.

5. Describe each transformation y = |f(x|| y = f(|x|) 6. Using the graph of f(x) sketch each transformation y = |f(x)| y = f(|x|) y = f(x) y = |f(x)| y = f(|x|) y = f(x)

In problems 7 & 8, write an equation for each piece-wise function:

Let c be a positive real number. Complete the following representations ns of shifts in the graph of y = f (x) : Example 1: Let f (x) = x. Write the equation for the function resulting from a vertical shift of 3 units downward and a horizontal shift of 2 units to the right of the graph of f (x). III. Reflecting Graphs (Pages 45−46) A reflection in the x-axis is a type of transformation of the graph of y = f(x) represented by h(x) = s ssss. A reflection in the y-axis is a type of transformation of the graph of y = f(x) represented by h(x) = sss ss. Example 2: Let f (x) = x. Describe the graph of g(x) = − x in terms of f. sss sssss ss s ss s ssssssssss Description 1) Vertical shift c units upward: 2) Vertical shift c units downward: 3) Horizontal shift c units to the right: 4) Horizontal shift c units to the left: TransformationFunction Notation

Be able to discuss a type of function A quadratic function is a polynomial function of ___________ degree. The graph of a quadratic function is a special “U”-shaped curve called a(n) _____________. The general equation of a quadratic is __________________ and the vertex is given as ____________. If the leading coefficient of a quadratic function is positive, the graph of the function opens _________ and the vertex of parabola is the __________ point on the graph. If the leading coefficient of a quadratic function is negative, the graph of the function opens __________ and the vertex of the parabola is the ___________ point on the graph. The standard form of a quadratic function is __________________ For a quadratic function in standard form, the axis of reflection of the associated parabola is the line _________ and the vertex is ________ To write a quadratic function in standard form,... To find the x--intercepts of the graph of f (x) = ax 2 + bx + c,... You can always use the quadratic formula, __________________ and sometimes you can factor

Sketch the graph of f (x) = x 2 + 2x − 8 and identify the vertex, axis, and x-intercepts of the parabola. No calculator For a quadratic function in the form f (x) = ax 2 + bx + c, when a > 0, f has a minimum that occurs at s ssssss s. When a < 0, f has a maximum that occurs at s ssssss s. To find the minimum or maximum value, ssssssss sss s ssssssss ss s ssssss. Example 2: Find the minimum value of the function f (x) = 3x2 −11x At what value of x does this minimum occur? sssssss ssssssss sssss ss sssss ssss Calculator

Which transformations make even function

Give a transformation which would make this an odd function

Let c be a positive real number. Complete the following representations ns of shifts in the graph of y = f (x) : 1) Vertical shift c units upward: _______________ 2) Vertical shift c units downward: ______________ 3) Horizontal shift c units to the right: _____________ 4) Horizontal shift c units to the left: _____________ Example 1: Let f (x) = x. Write the equation for the function resulting from a vertical shift of 3 units downward and a horizontal shift of 2 units to the right of the graph of f (x). III. Reflecting Graphs (Pages 45−46) A reflection in the x-axis is a type of transformation of the graph of y = f(x) represented by h(x) = s ssss. A reflection in the y-axis is a type of transformation of the graph of y = f(x) represented by h(x) = sss ss. Example 2: Let f (x) = x. Describe the graph of g(x) = − x in terms of f. sss sssss ss s ss s ssssssssss

Name three types of rigid transformations: 1) ssssssssss ssssss 2) ssssssss ssssss 3) sssssssssss Rigid transformations change only the ssssssss of the graph in the coordinate plane. Name four types of nonrigid transformations: 1) ssssssss sssssss 2) ssssssss ssssssssssssssss ssssssssssssssss sssssss 3) 4) sssssssssss A nonrigid transformation tion y = cf (x) of the graph of y = f (x) is a ssssssss sssssss if c > 1 or a ssssssss sssss if 0 < c < 1. A nonrigid transformation y= f(cx) of the graph of y = f (x) is a ssssssssss ssssss if c > 1 or a ssssssssss sssssss if 0 < c < 1.