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)

x

y

x

y

x

y

x

y

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:

Transformation Function 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) = ax2 + bx + c , . . .

You can always use the quadratic formula, __________________

and sometimes you can factor

Sketch the graph of f (x) = x2 + 2x − 8 andidentify the vertex, axis, and x-intercepts of theparabola.

No calculator

For a quadratic function in the form f (x) = ax2 + bx + c , whena > 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 sssssssss ss s ssssss .Example 2: Find the minimum value of the functionf (x) = 3x2 −11x + 16 . At what value of x doesthis 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 ssssss2) ssssssss ssssss3) sssssssssssRigid transformations change only the ssssssss of thegraph in the coordinate plane.Name four types of nonrigid transformations:1) ssssssss sssssss2) ssssssss ssssssssssssssss ssssssssssssssss sssssss3)4) sssssssssssA nonrigid transformation tion y = cf (x) of the graph of y = f (x) isa ssssssss sssssss if c > 1 or a ssssssss sssss if0 < c < 1. A nonrigid transformation y= f(cx) of the graph ofy = f (x) is a ssssssssss ssssss if c > 1 or assssssssss sssssss if 0 < c < 1.