TodayWarm Up: (3)

Review Last Khan Academy TopicFunction Notation: f(x)

Finding the x and y InterceptsClass Work 3.5 Distributed

Feb. 11

Write the rule for the function graphed below

Warm Up

Write the rule for the function graphed below

Warm Up

Y = 2x + 1

Class Notes Section of

Notebook, pls.

Function Notation:

f(x)..g(x)..h(x)The equation that represents a function is called a function rule.A function rule is written with two variables, x

and y. It can also be written in function notation, f(x). The f(x), or g(x), is simply a notation for the dependent variable.Functions that can be written as equations can be written in function notation. The variable y and the term f(x) represent the dependent variable. It is simply a way to show that the y variable is a function of, or depends on x. It is read "f at x"Since x can be any number, the f(x) is the output, (the dependent variable), when a number is substituted for x.If used on the same graph, different functions have different function notations f(x) or g(x) to avoid confusion, but both represent the y variable.

How to Evaluate a Function RuleTo evaluate a function rule, substitute the value in for x and solve for y.Examples: Evaluate the given function rules for x = 2

f(x)= x + 5

f(x)=(2)+ 5

y= 7

g(x) = 2(2)-1= 4 – 1

y= 3

h(x = -(2)+2= -2 + 2

y= 0

……….

h(x)= -x + 2

g(x)= 2x -1

Graphs of Linear

Equations

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Graphs of y = bWhere b is any number

y = b are always horizontal lines, and are functions

Graphs of x = aWhere a is any number

x = a are always vertical lines, and are not functions

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Graphs of y = mxy = "a number times x"

y = mx lines will always go through the origin, and will be at the angle shown.

Graphs of y = mx + cy = "a number times x plus c"

y = mx + c are similar in shape to y = mx,

but do not go through the origin.

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Defining Linear EquationsHOW DO I KNOW IF AN EQUATION IS LINEAR?

No bend or curve in the line.

Not Linear

If an equation is linear, the result is a straight line.

A line can be a function, and not be a linear function.

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Solutions to Linear EquationsTo ask "Is the ordered pair (1,3) a solution to the

equation y = 10x - 7?", is the same as asking, " Is the point (1,3) on the line of y = 10x -7"? How do we know?

Determine whether the following ordered pairs are solutions to the equation y = 10x -7 a. (1,3) b. (2, 13) c. (-1,-3)

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These are the x- and y-Intercepts

The x-intercept is where the graph crosses the x-axis. The y-coordinate is always zero.

The y-intercept is where the graph crosses the y-axis.

The x-coordinate is always zero.

(2, 0)

(0, -6)Being able to locate the intercepts makes it easy to

draw the line associated with the given equation.

Formulas:

Standard Form of a linear equation:Ax + By = CA, B, & C are all constants

and.. a.) A and B are not both zero. b.) The largest exponent is not greater than 1Change to Standard

Form:4y + 12 = 6xThe Standard Form of a linear

equation is used when you want to find the intecepts of a line

Formulas: Standard Form of a linear equation:Ax + By = C

The 'x' variable is first..

We use our knowledge of coordinate values and intercepts to find where (if) the line crosses both axes. Not all lines cross both axes.

The Standard Form of 4y + 12 = 6x is..

At the x intercept, y is always zero. The ordered pair is (x, 0).

6x - 4y = 12

The equation to find the x intercept then, is 6x - 4(0) = 12.6x = 12, x = 2. The x intercept coordinates are (2,0)Find the y intercept.

6(0) -4y = 12y = -3 The y intercept

coordinates are (0,-3)

Graph the intercepts and draw the line

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To find the x-intercept: Plug in 0 for y since y is always 0 at the x-intercept.

x - 2(0) = 12x = 12; (12, 0)

y-intercept: Plug in 0 for x.0 - 2y = 12

y = -6; (0, -6)

Find the x- and y-intercepts.1. x - 2y = 12

x-intercept: Plug in 0 for y.Does 0 = 7?

No! There is no x-intercept. NoneWhat type of lines have no x-intercept?

Horizontal!Horizontal lines…y = 7…y-int = (0, 7)

Find the x- and y-intercepts.3. y = 7 ***Special case***

x-intercept: Plug in 0 for y.-3x - 5(0) = 9

-3x = 9x = -3; (-3, 0)

y-intercept: Plug in 0 for x.-3(0) + 5y = 9

5y = 9y = ; (0, )

Find the x- and y-intercepts.2. -3x + 5y = 9

𝟗𝟓

What is the x-intercept of3x – 4y = 24?

1. (3, 0)2. (8, 0)3. (0, -4)4. (0, -6)

What is the y-intercept of

-x + 2y = 8?

1. (-1, 0)2. (-8, 0)3. (0, 2)4. (0, 4)

What is the y-intercept ofx = 3?

1. (3, 0)2. (-3, 0)3. (0, 3)4. None

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Class Work: CW 3.4; Due Today

CW 3.5; due date is now 02/16/16

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Finding the x-and y-intercepts of Linear Equations

The path of the defender crosses the path of the thrown football.

In algebra, what are x- and y-intercepts?

What does it mean to INTERCEPT a pass in football?