Domain and Range of Quadratic Functions. What patterns do we see? When we are trying to figure out...
-
Upload
kimberly-rich -
Category
Documents
-
view
216 -
download
1
Transcript of Domain and Range of Quadratic Functions. What patterns do we see? When we are trying to figure out...
![Page 1: Domain and Range of Quadratic Functions. What patterns do we see? When we are trying to figure out the domain of any function the question we should ask.](https://reader036.fdocuments.in/reader036/viewer/2022082610/56649db95503460f94aa99db/html5/thumbnails/1.jpg)
Domain and Range of Quadratic Functions
![Page 2: Domain and Range of Quadratic Functions. What patterns do we see? When we are trying to figure out the domain of any function the question we should ask.](https://reader036.fdocuments.in/reader036/viewer/2022082610/56649db95503460f94aa99db/html5/thumbnails/2.jpg)
What patterns do we see?
• When we are trying to figure out the domain of any function the question we should ask ourselves is:
• What possible values could this function take on for x?
• We can ask the same question for range.• What possible values could this function
take on for y?
![Page 3: Domain and Range of Quadratic Functions. What patterns do we see? When we are trying to figure out the domain of any function the question we should ask.](https://reader036.fdocuments.in/reader036/viewer/2022082610/56649db95503460f94aa99db/html5/thumbnails/3.jpg)
What patterns do we see?
• Sometimes people get confused and state domain and range in terms of what a function cannot be. THIS IS WRONG!!
• Always state the domain and range in terms of what can be!!
![Page 4: Domain and Range of Quadratic Functions. What patterns do we see? When we are trying to figure out the domain of any function the question we should ask.](https://reader036.fdocuments.in/reader036/viewer/2022082610/56649db95503460f94aa99db/html5/thumbnails/4.jpg)
What patterns do we see?
• Unless a parabola has dots at its end or we are specifically told that it does not continue to extend indefinitely, we can make the presumtion that it will always have the same domain: x
![Page 5: Domain and Range of Quadratic Functions. What patterns do we see? When we are trying to figure out the domain of any function the question we should ask.](https://reader036.fdocuments.in/reader036/viewer/2022082610/56649db95503460f94aa99db/html5/thumbnails/5.jpg)
Why is this?
• Think about it: As we move up from the vertex of (0,0) we notice that the parabola continues to get wider and wider. This pattern will continue forever. So there will be no restriction on what x can possibly be.
![Page 6: Domain and Range of Quadratic Functions. What patterns do we see? When we are trying to figure out the domain of any function the question we should ask.](https://reader036.fdocuments.in/reader036/viewer/2022082610/56649db95503460f94aa99db/html5/thumbnails/6.jpg)
What about the range?
• The range will change from graph to graph• We can see from the previous graph that it
will never go below the y value of “0”. • Therefore, y can only be greater than 0. • It will still belong to real numbers because
there is an unbroken line connecting all the points. In short:
yyR ,0:
![Page 7: Domain and Range of Quadratic Functions. What patterns do we see? When we are trying to figure out the domain of any function the question we should ask.](https://reader036.fdocuments.in/reader036/viewer/2022082610/56649db95503460f94aa99db/html5/thumbnails/7.jpg)
Another Example
• Find the domain and range of the following:
}{:
}5,{:
yeRR
xxeRD
![Page 8: Domain and Range of Quadratic Functions. What patterns do we see? When we are trying to figure out the domain of any function the question we should ask.](https://reader036.fdocuments.in/reader036/viewer/2022082610/56649db95503460f94aa99db/html5/thumbnails/8.jpg)
Real World Applications
• Imagine the height of a ball thrown off a building is modelled by the equation
• Where t is time in seconds and h is height in meters
• What would be an appropriate domain and range?
15)2(5.0)( 2 xth
![Page 9: Domain and Range of Quadratic Functions. What patterns do we see? When we are trying to figure out the domain of any function the question we should ask.](https://reader036.fdocuments.in/reader036/viewer/2022082610/56649db95503460f94aa99db/html5/thumbnails/9.jpg)
Real World Applications
We can see that the x intercepts are approximately –3.5 and +7.5. However, it is not realistic to have negative time therefore we would modify the domain to:
},5.70{: RttD
![Page 10: Domain and Range of Quadratic Functions. What patterns do we see? When we are trying to figure out the domain of any function the question we should ask.](https://reader036.fdocuments.in/reader036/viewer/2022082610/56649db95503460f94aa99db/html5/thumbnails/10.jpg)
Real World Applications
},150{: RhhR
Similarly, it wouldn’t make sense for the ball to go below ground so the range would be as follows:
![Page 11: Domain and Range of Quadratic Functions. What patterns do we see? When we are trying to figure out the domain of any function the question we should ask.](https://reader036.fdocuments.in/reader036/viewer/2022082610/56649db95503460f94aa99db/html5/thumbnails/11.jpg)
Pop Quiz
• Find the Domain and Range of the following relations.
![Page 12: Domain and Range of Quadratic Functions. What patterns do we see? When we are trying to figure out the domain of any function the question we should ask.](https://reader036.fdocuments.in/reader036/viewer/2022082610/56649db95503460f94aa99db/html5/thumbnails/12.jpg)
Graph 1 Graph 2
![Page 13: Domain and Range of Quadratic Functions. What patterns do we see? When we are trying to figure out the domain of any function the question we should ask.](https://reader036.fdocuments.in/reader036/viewer/2022082610/56649db95503460f94aa99db/html5/thumbnails/13.jpg)
Graph 3 Graph 4
![Page 14: Domain and Range of Quadratic Functions. What patterns do we see? When we are trying to figure out the domain of any function the question we should ask.](https://reader036.fdocuments.in/reader036/viewer/2022082610/56649db95503460f94aa99db/html5/thumbnails/14.jpg)
Graph 5
Answers:
1.
2.
3.
4.
5.
}{:
}{:
yeRR
xeRD
}8,{:
}{:
yyeRR
xeRD
}91,{:
}91,{:
yyeRR
xxeRD
}{:
}8,{:
yeRR
xXeRD
}6,3,1,3,5{:
}4,3,2,1,3,6{:
R
D
![Page 15: Domain and Range of Quadratic Functions. What patterns do we see? When we are trying to figure out the domain of any function the question we should ask.](https://reader036.fdocuments.in/reader036/viewer/2022082610/56649db95503460f94aa99db/html5/thumbnails/15.jpg)
So in conclusion:• Don’t just apply a blanket idea to
everything…..look at the circumstances as well.