Relations and Functions
What makes a relation a Function?
Every element of the domain is paired with exactly 1 element of the range
f(x)=2x+1
f(5)
f(5)=11
Write in standard form
2y=3x-10
3x-2y=10
Write an equation in point slope form
Point= (3,-2)
Slope -2
(y+2)=-2(x-3)
Solving Using Graphing
y=2x+1
y=-x+7
(2,5)
Determine if the following is a relation, function, both or neither.
{(3,2),(2,3),(4,5),(6,2)}
Both
f(x)=1/3x-3
f(12)
f(12)=1
Write in slope intercept form
3x+2y=14
y=-3/2x+7
Write in point slope form
(2,-2)
m=-2
y+2=-2(x-2)
Solve using elimination
-3x+2y=56
5x+2y=-24
(-10, 13)
Determine if the following is a Relation, Function, Neither, or Both.
9x
Neither
f(x)=3x-1
f(1)*f(3)
f(1)=2
f(3)=8
f(1)*f(3)=16
Determine the slope
3x+2y=12
m=-3/2
Write in slope intercept form
y-2=3(x-2)
y=3x-4
Solve using Substitution
x+y=14
-3y=3x+21
No Solution
Determine if the following is Discrete or Continuous.
y=2x+1
Continuous
f(x)=-2/5x+11
f(x)=3
x=20
Write in standard form
10x+20y=100
x+2y=10
Find the equation of the line and put in point slope form
(3,2), (2,3)
(y-3)=-1(x-2)
or
(y-2)=-1(x-3)
Solve using graphing:
y=x-2
y=4
(6, 4)
Determine the domain and range of the Following function, if any.
2y-2x=0
y=x
Domain=All Real Number
Range=All Real Numbers
g(x)=x^2+2x-1
g(a+1)
a^2+2a+1+2a+2-1
a^2+4a+2
Determine Parallel, Perpendicular or Neither
3x+3y=18
And
(4,2), (-1,-3)
Perpendicular
Write the equation in slope intercept form
(-2,3), (4,6)
y=1/2x+4
Solve Using Any Method
y=3x+10
2y+x=20
(0, 10)
Solve the following:
x+2y-z=6
2x+y+z=9
3x+4y+z=18
(3,2,1)