Functions and Their Graphs 5 basic graphs Formula: 1) y = x 2) y = x² 3) y = x³ 4) y = √x 5) y =...
-
Upload
arleen-hudson -
Category
Documents
-
view
223 -
download
0
Transcript of Functions and Their Graphs 5 basic graphs Formula: 1) y = x 2) y = x² 3) y = x³ 4) y = √x 5) y =...
![Page 1: Functions and Their Graphs 5 basic graphs Formula: 1) y = x 2) y = x² 3) y = x³ 4) y = √x 5) y = |x| Graph: 1) Linear— “line” 2) Quadratic— “parabola”](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f2b5503460f94c4654f/html5/thumbnails/1.jpg)
Functions and Their Graphs
![Page 2: Functions and Their Graphs 5 basic graphs Formula: 1) y = x 2) y = x² 3) y = x³ 4) y = √x 5) y = |x| Graph: 1) Linear— “line” 2) Quadratic— “parabola”](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f2b5503460f94c4654f/html5/thumbnails/2.jpg)
5 basic graphs
Formula:
1) y = x
2) y = x²
3) y = x³
4) y = √x
5) y = |x|
Graph:
1) Linear— “line”
2) Quadratic— “parabola”
3) Cubic— “squiggly”
4) Square Root– “half of a parabola
5) Absolute Value– “V-shaped”
![Page 3: Functions and Their Graphs 5 basic graphs Formula: 1) y = x 2) y = x² 3) y = x³ 4) y = √x 5) y = |x| Graph: 1) Linear— “line” 2) Quadratic— “parabola”](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f2b5503460f94c4654f/html5/thumbnails/3.jpg)
Shiftsy = a(x - h)²+k
h is the horizontal shift. The graph will move in the opposite direction.
K is the vertical shift. The graph will move in the same direction.
If a is positive, then the graph will go up. If a is negative, then the graph will go down.
![Page 4: Functions and Their Graphs 5 basic graphs Formula: 1) y = x 2) y = x² 3) y = x³ 4) y = √x 5) y = |x| Graph: 1) Linear— “line” 2) Quadratic— “parabola”](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f2b5503460f94c4654f/html5/thumbnails/4.jpg)
If a is positive, then the graph will go up.
If a is negative, then the graph will go down.
![Page 5: Functions and Their Graphs 5 basic graphs Formula: 1) y = x 2) y = x² 3) y = x³ 4) y = √x 5) y = |x| Graph: 1) Linear— “line” 2) Quadratic— “parabola”](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f2b5503460f94c4654f/html5/thumbnails/5.jpg)
More info about parabolasy = a(x – h)² + k
![Page 6: Functions and Their Graphs 5 basic graphs Formula: 1) y = x 2) y = x² 3) y = x³ 4) y = √x 5) y = |x| Graph: 1) Linear— “line” 2) Quadratic— “parabola”](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f2b5503460f94c4654f/html5/thumbnails/6.jpg)
The Vertex of a Parabolay = a(x – h)² + k
The vertex is (h, k). In other words, the vertex is (H.S., V.S). For example, y = (x – 2)² – 9. H.S. = Right 2 V.S. = Down 9 Therefore, the vertex is denoted by V(2, -9).
![Page 7: Functions and Their Graphs 5 basic graphs Formula: 1) y = x 2) y = x² 3) y = x³ 4) y = √x 5) y = |x| Graph: 1) Linear— “line” 2) Quadratic— “parabola”](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f2b5503460f94c4654f/html5/thumbnails/7.jpg)
For example: y = x² + 6
y = (x – 0)² + 6, so the V.S. is up 6 and the H.S. is none. Therefore, the vertex is
V (0, 6). Since a is positive, the direction of the
parabola is up. Since a is 1, then the parabola is neither fat
or skinny. It is a standard parabola.
![Page 8: Functions and Their Graphs 5 basic graphs Formula: 1) y = x 2) y = x² 3) y = x³ 4) y = √x 5) y = |x| Graph: 1) Linear— “line” 2) Quadratic— “parabola”](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f2b5503460f94c4654f/html5/thumbnails/8.jpg)
Another example: y = 2(x + 2)² + 6
H.S. = left 2 V.S. = up 6 V (–2, 6) Direction is up Since a = 2, then the parabola is skinny
![Page 9: Functions and Their Graphs 5 basic graphs Formula: 1) y = x 2) y = x² 3) y = x³ 4) y = √x 5) y = |x| Graph: 1) Linear— “line” 2) Quadratic— “parabola”](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f2b5503460f94c4654f/html5/thumbnails/9.jpg)
Axis of Symmetry of a Parabolay = a(x – h)² + k
x = H.S. or x = h
For example, y = (x – 2)²– Axis of symmetry is x = 2
![Page 10: Functions and Their Graphs 5 basic graphs Formula: 1) y = x 2) y = x² 3) y = x³ 4) y = √x 5) y = |x| Graph: 1) Linear— “line” 2) Quadratic— “parabola”](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f2b5503460f94c4654f/html5/thumbnails/10.jpg)
Practice
up or down? fat or skinny? V.S.? H.S.? Axis Symmetry: Graph it
21f(x)= x+4 -52
![Page 11: Functions and Their Graphs 5 basic graphs Formula: 1) y = x 2) y = x² 3) y = x³ 4) y = √x 5) y = |x| Graph: 1) Linear— “line” 2) Quadratic— “parabola”](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f2b5503460f94c4654f/html5/thumbnails/11.jpg)
Practice 21f(x)= x+4 -52
![Page 12: Functions and Their Graphs 5 basic graphs Formula: 1) y = x 2) y = x² 3) y = x³ 4) y = √x 5) y = |x| Graph: 1) Linear— “line” 2) Quadratic— “parabola”](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f2b5503460f94c4654f/html5/thumbnails/12.jpg)
Practicey = -|x – 6| + 3
What does this graph look like? Horizontal shift? Vertical shift? Vertex? Fat or skinny? Up or down?
![Page 13: Functions and Their Graphs 5 basic graphs Formula: 1) y = x 2) y = x² 3) y = x³ 4) y = √x 5) y = |x| Graph: 1) Linear— “line” 2) Quadratic— “parabola”](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f2b5503460f94c4654f/html5/thumbnails/13.jpg)
Practicey = -|x – 6| + 3
![Page 14: Functions and Their Graphs 5 basic graphs Formula: 1) y = x 2) y = x² 3) y = x³ 4) y = √x 5) y = |x| Graph: 1) Linear— “line” 2) Quadratic— “parabola”](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f2b5503460f94c4654f/html5/thumbnails/14.jpg)
Practicey = (x + 1)³ - 5
What does this graph look like? H.S.? V.S.? There is no vertex. Right or Left? Fat or skinny?
![Page 15: Functions and Their Graphs 5 basic graphs Formula: 1) y = x 2) y = x² 3) y = x³ 4) y = √x 5) y = |x| Graph: 1) Linear— “line” 2) Quadratic— “parabola”](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f2b5503460f94c4654f/html5/thumbnails/15.jpg)
Practicey = (x + 1)³ - 5
![Page 16: Functions and Their Graphs 5 basic graphs Formula: 1) y = x 2) y = x² 3) y = x³ 4) y = √x 5) y = |x| Graph: 1) Linear— “line” 2) Quadratic— “parabola”](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f2b5503460f94c4654f/html5/thumbnails/16.jpg)
Practice
What does this graph look like? H.S.? V.S.? There is no vertex. Up or down? Fat or skinny?
2 5y x
![Page 17: Functions and Their Graphs 5 basic graphs Formula: 1) y = x 2) y = x² 3) y = x³ 4) y = √x 5) y = |x| Graph: 1) Linear— “line” 2) Quadratic— “parabola”](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f2b5503460f94c4654f/html5/thumbnails/17.jpg)
Practice 2 5y x
![Page 18: Functions and Their Graphs 5 basic graphs Formula: 1) y = x 2) y = x² 3) y = x³ 4) y = √x 5) y = |x| Graph: 1) Linear— “line” 2) Quadratic— “parabola”](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f2b5503460f94c4654f/html5/thumbnails/18.jpg)
Domain and Range
Domain is the set of all x-values. You will look at the graph from left to right (like you’re reading a book). Ask yourself: where does the graph begin? Where does it end?
Range is the set of all y-values. You will look at the graph from bottom to top. Ask yourself: where does the graph begin? Where does it end?
![Page 19: Functions and Their Graphs 5 basic graphs Formula: 1) y = x 2) y = x² 3) y = x³ 4) y = √x 5) y = |x| Graph: 1) Linear— “line” 2) Quadratic— “parabola”](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f2b5503460f94c4654f/html5/thumbnails/19.jpg)
![Page 20: Functions and Their Graphs 5 basic graphs Formula: 1) y = x 2) y = x² 3) y = x³ 4) y = √x 5) y = |x| Graph: 1) Linear— “line” 2) Quadratic— “parabola”](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f2b5503460f94c4654f/html5/thumbnails/20.jpg)
Find the domain and range.
From left to right, while following the x-axis, where does the graph begin? Where does it end?
From bottom to top, while following the y-axis, where does the graph begin? Where does it end?
![Page 21: Functions and Their Graphs 5 basic graphs Formula: 1) y = x 2) y = x² 3) y = x³ 4) y = √x 5) y = |x| Graph: 1) Linear— “line” 2) Quadratic— “parabola”](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f2b5503460f94c4654f/html5/thumbnails/21.jpg)
Answer:
![Page 22: Functions and Their Graphs 5 basic graphs Formula: 1) y = x 2) y = x² 3) y = x³ 4) y = √x 5) y = |x| Graph: 1) Linear— “line” 2) Quadratic— “parabola”](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f2b5503460f94c4654f/html5/thumbnails/22.jpg)
Symmetry
![Page 23: Functions and Their Graphs 5 basic graphs Formula: 1) y = x 2) y = x² 3) y = x³ 4) y = √x 5) y = |x| Graph: 1) Linear— “line” 2) Quadratic— “parabola”](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f2b5503460f94c4654f/html5/thumbnails/23.jpg)
Symmetry
![Page 24: Functions and Their Graphs 5 basic graphs Formula: 1) y = x 2) y = x² 3) y = x³ 4) y = √x 5) y = |x| Graph: 1) Linear— “line” 2) Quadratic— “parabola”](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f2b5503460f94c4654f/html5/thumbnails/24.jpg)
Symmetry
![Page 25: Functions and Their Graphs 5 basic graphs Formula: 1) y = x 2) y = x² 3) y = x³ 4) y = √x 5) y = |x| Graph: 1) Linear— “line” 2) Quadratic— “parabola”](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f2b5503460f94c4654f/html5/thumbnails/25.jpg)
Symmetry
![Page 26: Functions and Their Graphs 5 basic graphs Formula: 1) y = x 2) y = x² 3) y = x³ 4) y = √x 5) y = |x| Graph: 1) Linear— “line” 2) Quadratic— “parabola”](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f2b5503460f94c4654f/html5/thumbnails/26.jpg)
Any questions?