Transcript FUNCTION

Chapter 8 Review
Section 8.1 “Relations and Functions”
RELATION
a pairing of numbers from one set, called the
DOMAIN, with the numbers in another set, called
the RANGE.
Set 1
Set 2
Domain
Input
Range
Output
X-coordinate
Y-coordinate
FUNCTIONIs a relation in which for each input there is
EXACTLY ONE output.
FUNCTION
2
4
6
8
0
1
0
1
NOT A FUNCTION
3
5
5
1
2
3
Each input must be paired with only
ONE output
Solving Linear Equations

To find a SOLUTION, substitute the
ordered pair into the equation and see if it
produces a true statement.
2x – y = 5
Tell whether the ordered pair is a solution to the equation.
point
NO
YES
(1, 3)
(2,-1)
equation
substitution
2x - y = 5
2(1) – 3 = 5
2x - y = 5
2(2) – -1 = 5
check
-1 = 5
5=5
Linear Equationan equation whose graph is a line
4x + y = 9
Function formAn equation is in function form when
the equation is solved for y.
4x + y = 9
y = 9 – 4x
Solve the equation for y.
Section 8.3 “Using Intercepts”
x-intercept-
y-intercept-
the x-coordinate of the
point where the graph
crosses the x-axis
the y-coordinate of the
point where the graph
crosses the y-axis
To find the x-intercept,
solve for ‘x’ when ‘y = 0.’
Find the x-intercept of the
graph
2x + 7y = 28.
2x + 7(0)= 28
2x = 28
x = 14
To find the y-intercept,
solve for ‘y’ when ‘x = 0.’
Find the y-intercept of the
graph
2x + 7y = 28.
2(0)+ 7y= 28
7y = 28
y=4
Section 8.4 “The Slope of a Line”
SLOPEthe ratio of the vertical change (the rise) to
the horizontal change (the run) between
any two points on a line.
Slope =
rise = change in y
run
change in x
Slope Review
The slope m of a line passing through two points
( x1 , y1 ) and ( x2 , y2 )
is the ratio of the rise
change to the run.
y
m
( y2  y1 )
( x2  x1 )
run
( x2 , y2 )
rise
( x1 , y1 )
x
Section 8.5 “Graph Using
Slope-Intercept Form”
SLOPE-INTERCEPT FORMa linear equation written in the form
y-coordinate
x-coordinate
y = mx + b
slope
y-intercept
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 Lines
two lines in the same plane are perpendicular if
they intersect at right angles. Because slope gives
the rate at which a line rises or falls, two lines with
slopes that are NEGATIVE RECIPROCALS are
PERPENDICULAR.
½ and -2 are
negative reciprocals.
4/3 and -3/4
are negative reciprocals.
y = -2x + 2
y = 1/2x – 4
Section 8.6 “Writing Linear Equations”
You can write a linear equation in slopeintercept form, if you know the slope (m) and
the y-intercept (b) of the equation’s graph.
SLOPE-INTERCEPT FORMa linear equation written in the form
y-coordinate
slope
x-coordinate
y = mx + b
y-intercept
Write an equation of the line that passes
through the given points. (-6, 0), (0, -24)
STEP 1
Calculate the slope of the line that
passes through (-6, 0) and (0, -24).
STEP 2
Write an equation of the line. The
line crosses the y-axis at (0, -24). So,
the y-intercept is -24.
y = mx + b
Write slope-intercept form.
y = -4x + (-24)
Substitute -4 for m and -24 for b.
The equation is y = -4x – 24.
Section 8.7 “Function Notation”
Function Notationa linear function written in the form
y = mx + b where y is written as a function f.
x-coordinate
This is read
as ‘f of x’
f(x) = mx + b
slope
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
y-intercept
Linear Functions
What is the value of the function
f(x) = 3x – 15 when x = -3?
A. -24
B. -6
C. -2
f(-3) = 3(-3) – 15
Simplify
f(-3) = -9 – 15
f(-3) = -24
D. 8
Linear Functions
For the function f(x) = 2x – 10, find the
value of x so that f(x) = 6.
f(x) = 2x – 10
Substitute into the function
6 = 2x – 10
Solve for x.
8 = x
When x = 6, f(x) = 8