Functions and Relations
How do we know a relation is a function?
we know a relation is a function if every input (x) has exactly one output (y)
1. 3x + 4 = 5x + 2
1. X = 1
simplify the problem
1. (w2)8
2. (a4)4
1. w16
2. a16
1) How do you find slope from a graph.
2) How do you find slope when given two points.
(Remember that these are formulas that we have learned.)
1. Rise/ Run
2. y2 - y1 / x2 - x1
What is this number written in standard form
1) 6.8 x 10-4
1) 0.00068
(-8 ,5) , (-5 , 8 ) , (8 , -5 ), (5 , -8)
Is this set of ordered pairs a function and why?
Yes, this is a function because every input has one output
What is the value of x in the following equation?
1. 5x − 2+ x=9 +3x + 10
x = 7
Simplify the following problems
1. 32 x 3-5 =
2. 42 x 4-4 =
1. 3-3
2. 4-2
Find the slope when given the two points below.
1) (-5 , 2) and (-8, 2)
1) Slope = 0
Write this number in Scientific Notation
1) 4850000
4.85 x 106
What are some different ways that we can represent functions?
1. From a graph
2. From an X and Y table
3. Arrow chart
What is the value of x in the following equation?
1) 37 = −3 + 5(x + 6)
x = 2
Simplify the following problems
1. 43 / 42
2. x8 / x4
1. 41 or 4
2. x4
Find the slope of the line through each pair of points.
1) (19, −16) and (−7, −15)
1) -1/26
Write this number in standard form
1) 4.85 x 105
1) 485000
What are the two different types of functions when looking at a graph?
1. Linear
2. non- linear
What is the value of x in the equation below?
1) 8 = 8v − 4(v + 8)
v = 10
Simplify the following exponents
1) 4-3
2) 1 / 4-3
1) 1 / 43
2. 43
Find the slope of the line through each pair of points.
1) (−4, 7) and (−6, −4)
1) 11 / 2
write the number in scientific Notation.
1) 0.0000068
1) 6.8 x 10-6
if given the following function notation
f(x) = 4x -1
What would be the outputs for these inputs given?
1. x = 3
2. x = -5
1. The output would be 11
2. The output would be -21
What is the value of x in the following equation?
1) −5n − 8(1 + 7n) = −8
n = 0
simplify the following exponents
1) 150
2) 25001540
1) 1
2) 1
1) (17, −13) and (17, 8)
1) Undefined
write the number in standard form
1) 4.8 x 105
1) 480000