Algebra I Regents Review - Graphs of Functions

Regents Review Lesson #4: Graphs of Functions

Homework: Topical Review Packet #2 (due Friday)

Warm Up Modeled off of January 2015 regents #21

Many short answer questions will require graphing. In those situations, always follow the same strategy for creating your graph:

1) Use your calculator to create a table.

2) Plot the points and connect them.

Do not just draw the shape without plotting specific points!

Note: For quadratics and absolute value functions, make sure you put the vertex in the center of your table.

x y

-2-10

-3-4

Algebra I Regents Review - Graphs of Functions

Review of Linear Functions:

* constant rate of change

y = mx + b

slope y-intercept

Mother function:

General form of linear functions:

Example:

y = x + 5-23

Review of Quadratic Functions: Mother function:

Standard Form:

y = ax2 + bx + C

Vertex Form:

y = (x - h)2 + k

Example:Standard form:

f(x) = 2x2 - 4x + 5

Vertex form:

f(x) = 2(x - 1)2 + 3

Algebra I Regents Review - Graphs of Functions

f(x) = 2x

y = abx

Initial Value

(y - intercept)

Base

(multiplier)

y = 3(2)x

y value doubles after each x

Review of Exponential Functions:

Review of Absolute Value Functions:

Mother function:

Algebra I Regents Review - Graphs of Functions

All functions can be "transformed" vertically and/or horizontally.

Basic Rules:

Horizontal transformations occur inside parentheses, square roots, absolute value signs, etc. They follow these rules:

g(x) = f(x + c) shifts the graph left/right (IHOP!)

g(x) = f(kx) makes the graph shrink horizontally if k is bigger than 1; stretch horizontally if k is between 0 and 1.

g(x) = f(-x) flips across the y axis. (horizontally)

Specific examples - identify the parent function and the transformation

y = |x + 3| y = √3x y = (-.5x2)

Vertical transformations occur outside parentheses, square roots, absolute value signs, etc. They follow these rules:

g(x) = f(x) + c shifts the graph up/down

g(x) = kf(x) makes the graph stretch vertically if k is bigger than 1; shrink vertically if k is between 0 and 1.

g(x) = -f(x) flips across the x axis. (vertically)

Specific examples - identify the parent function and the transformation

y = |x| - 2 y = .25√x y = -x2 + 3

Algebra I Regents Review - Graphs of Functions

Domain: The x values that create a function

Ex:

0 ≤ x < ∞

or

[0 , ∞ )

Lowest x valueIncludes this endpoint

Doesn't include this endpoint Highest x value

* The x-values from 0 to infinity, including 0.

Range: The outputs of a function

Ex:

4 ≤ y ≤ 20

or

[ 4 , 20 ]

Lowest x valueIncludes this endpoint

Highest x value

* The y-values from 4 to 20, including both.

Algebra I Regents Review - Graphs of Functions

Piecewise function - Different function rules for each interval.

Things to remember: Don't connect lines that don't meet.

Make separate tables for each rule and watch for open circles.

x

-2

-1

0

y

4

1

0

x

0

1

2

3

y

2

2

2

2

y

1

0

-1

x

3

4

5

Sample Regents Question

Algebra I Regents Review - Graphs of Functions

Sample Regents Question

Sample Regents Question

Algebra I Regents Review - Graphs of Functions

Sample Regents Question

Sample Regents Question

Algebra I Regents Review - Graphs of Functions

Sample Regents Question

Sample Regents Question

Algebra I Regents Review - Graphs of Functions

Sample Regents Question

Sample Regents Question

Algebra I Regents Review - Graphs of Functions

Sample Regents Question

Sample Regents Question

Algebra I Regents Review - Graphs of Functions

Sample Regents Question