60
Domain & Range

Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Embed Size (px)

Citation preview

Page 1: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 2: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Page 3: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

EXAMPLE : What is the range of the given function ?

Page 4: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

EXAMPLE : What is the range of the given function ?

Page 5: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

EXAMPLE : What is the range of the given function ?

Page 6: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

EXAMPLE #2 : What is the domain of the given function ?

Page 7: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

EXAMPLE #2 : What is the domain of the given function ?

Page 8: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

EXAMPLE #2 : What is the domain of the given function ?

Page 9: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 10: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 11: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Linear graphs have no holes in them and continue in either direction infinitely…

Page 12: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 13: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 14: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 15: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 16: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

A quadratic function is similar to a linear function…no holes or breaks in the graph

Page 17: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

A quadratic function is similar to a linear function…no holes or breaks in the graph

So the domain contains all real numbers…

Page 18: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 19: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 20: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 21: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 22: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 23: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 24: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 25: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 26: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 27: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 28: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 29: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 30: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Absolute Value :

Acts like a quadratic…

Page 31: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Absolute Value :

Acts like a quadratic…

Domain is all real numbers…

Page 32: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Absolute Value :

Acts like a quadratic…

Domain is all real numbers…

Range : Find the vertex and see which way the graph is pointing…

Page 33: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 34: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

What if only the function is given and not the graph ? How do you determine the domain and range ?

Page 35: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

What if only the function is given and not the graph ? How do you determine the domain and range ?

For all linear and cubic functions, both domain and range are all real numbers.

Page 36: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

What if only the function is given and not the graph ? How do you determine the domain and range ?

For all linear and cubic functions, both domain and range are all real numbers.

Quadratic and absolute value are the same…

Page 37: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 38: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 39: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 40: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 41: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 42: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 43: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 44: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 45: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 46: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 47: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 48: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 49: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 50: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 51: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 52: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 53: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 54: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 55: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 56: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 57: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 58: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 59: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range

Page 60: Domain & Range. When the coordinates are listed; determining the Domain ( D ) and Range ( R ) of a function is quite easy…

Domain & Range