Chapter 8 ReviewChapter 8 Review

RELATIONa pairing of numbers from one set, called the DOMAIN, with the numbers in another set, called the RANGE.

DomainDomain

InputInput

X-coordinateX-coordinate

RangeRange

OutputOutput

Y-coordinateY-coordinate

Set 1Set 1 Set 2Set 2

Section 8.1 “Relations and Functions”

FUNCTION-

Each input must be paired with Each input must be paired with only only ONEONE output output

Is a relation in which for each input there Is a relation in which for each input there is EXACTLY ONE output.is EXACTLY ONE output.

FUNCTIONFUNCTION

22446688

00110011

NOT A FUNCTIONNOT A FUNCTION

33

55

55112233

Solving Linear Equations To find a SOLUTION, substitute the

ordered pair into the equation and see if it produces a true statement.

2x – y = 52x – y = 5

2x - y = 52x - y = 5 22(1) (1) – – 33 = 5 = 5 -1 = 5-1 = 5equation substitution check

(1, 3)(1, 3)

Tell whether the ordered pair is a solution to the equation.

NO

2x - y = 52x - y = 5 22(2) (2) – – -1-1 = 5 = 5 5 = 55 = 5 (2,-1)(2,-1)YES

point

Linear Equation-an equation whose graph is a linean equation whose graph is a line

Function form-An equation is in function form An equation is in function form when the equation is solved for when the equation is solved for

y. y.

4x + y = 94x + y = 9

4x + y = 94x + y = 9 y = 9 – 4xy = 9 – 4xSolve the equation for y.

Section 8.3 “Using Intercepts”

x-intercept-

the x-coordinate of the x-coordinate of the point where the the point where the graph crosses the graph crosses the x-axisx-axis

To find the x-intercept, To find the x-intercept, solve for ‘x’ when ‘y = 0.’solve for ‘x’ when ‘y = 0.’

Find the x-intercept of the Find the x-intercept of the

graphgraph 2x + 7y = 282x + 7y = 28..

2x + 7(0)= 282x + 7(0)= 28

2x = 282x = 28

x = 14x = 14

y-intercept-the y-coordinate of the y-coordinate of the point where the the point where the graph crosses the graph crosses the y-axisy-axisTo find the y-intercept, To find the y-intercept, solve for ‘y’ when ‘x = 0.’solve for ‘y’ when ‘x = 0.’

Find the y-intercept of the Find the y-intercept of the

graphgraph 2x + 7y = 282x + 7y = 28..

2(0)+ 7y= 282(0)+ 7y= 28

7y = 287y = 28

y = 4y = 4

Section 8.4 “The Slope of a Line”

SLOPE-the ratio of the vertical change (the rise) to the horizontal change (the run) between any two points on a line.

Slope = Slope = rise rise = = change in ychange in y run change in xrun change in x

Slope Review

The slope m of a line passing through two points

and is the ratio of the rise change to the run.

),( 11 yx ),( 22 yx

m

y

x

),( 11 yx

),( 22 yx

runrun

riserise)( 12 yy

)( 12 xx

Section 8.5 “Graph Using Slope-Intercept Form”

SLOPE-INTERCEPT FORM-

a linear equation written in the form

y = mx + b

slope y-intercept

y-coordinate x-coordinate

Parallel Lines

two lines in the same plane are parallel if they never intersect. Because slope gives the rate at which a line rises or falls, two lines with the SAME SLOPE are PARALLEL.

y = 3x + 2

y = 3x – 4

Perpendicular LinesPerpendicular Lines

two lines in the same plane are perpendicular if two lines in the same plane are perpendicular if they intersect at right angles. Because slope gives they intersect at right angles. Because slope gives the rate at which a line rises or falls, two lines with the rate at which a line rises or falls, two lines with slopes that are slopes that are NEGATIVE RECIPROCALSNEGATIVE RECIPROCALS are are PERPENDICULARPERPENDICULAR..

y = y = -2-2x + 2x + 2

y = y = 1/21/2x – 4 x – 4

½ and -2 are ½ and -2 are negative reciprocals.negative reciprocals.

4/3 and -3/4 4/3 and -3/4 are negative reciprocals.are negative reciprocals.

Section 8.6 “Writing Linear Equations”

SLOPE-INTERCEPT FORM-

a linear equation written in the form

y = mx + bslope y-intercepty-coordinate x-coordinate

You can write a linear equation in slope-intercept form, if you know the slope (m) and the y-intercept (b) of the equation’s graph.

Write an equation of the line that passes through the given points. (-6, 0), (0, -24)

Calculate the slope of the line that passes through (-6, 0) and (0, -24).

STEP 1

y = mx + b Write slope-intercept form.

y = -4x + (-24) Substitute -4 for m and -24 for b.

Write an equation of the line. The line crosses the y-axis at (0, -24). So, the y-intercept is -24.

STEP 2

The equation is y = -4x – 24.

Section 8.7 “Function Notation”

Function Notation-a linear function written in the form y = mx + b where y is written as a function f.

f(x) = mx + bslope y-intercept

x-coordinate

f(x) is another name for y.It means “the value of f at x.”g(x) or h(x) can also be used to name functions

This is read as ‘f of x’

Linear FunctionsWhat is the value of the function What is the value of the function

f(x) = 3x – 15 when x = -3?f(x) = 3x – 15 when x = -3?

A. -24 B. -6 C. -2 D. 8A. -24 B. -6 C. -2 D. 8

f(f(-3-3) = 3() = 3(-3-3) – 15 ) – 15 Simplify

f(f(-3-3) = -9 – 15 ) = -9 – 15 f(f(-3-3) = -24 ) = -24

Linear Functions

For the function f(x) = 2x – 10, find the For the function f(x) = 2x – 10, find the value of value of xx so that f(x) = 6. so that f(x) = 6.

f(x)f(x) = 2x – 10 = 2x – 10 Substitute into the function

66 = 2x – 10 = 2x – 10

8 = x 8 = x Solve for x.

When x = 6, f(x) = 8When x = 6, f(x) = 8