1. What is the domain and range for the function f(x) = 𝟏 𝒙 ?
QQ:
Write the equation for a quadratic graph that has been stretched by a factor of 3 and shifted up 2.
What is the domain and range for the function
f(x) = 𝟏 𝒙 ?
Which of these is a quadratic function?
f(x) = x(x2 + 1) b) g(x) = x3 – x
c) h(x) = 0x2 – x d) k(x) = x(x -5)

2. QQ:
Write the equation for a quadratic graph that has been stretched by a factor of 3 with a vertical shift of 2.
y = 3x2 + 2

3. What is the domain and range for the function f(x) = 𝟏 𝒙 ?
QQ:
Write the equation for a quadratic graph that has been stretched by a factor of 3 and shifted up 2.
What is the domain and range for the function
f(x) = 𝟏 𝒙 ?
Which of these is a quadratic function?
f(x) = x(x2 + 1) b) g(x) = x3 – x
c) h(x) = 0x2 – x d) k(x) = x(x -5)

4. 2. What is the domain and range for the function f(x) = 𝟏 𝒙 ?
QQ:
2. What is the domain and range for the function
f(x) = 𝟏 𝒙 ?
Domain: (- ∞, 0) ⋃ (0, ∞)
Range: (-∞, 0) ⋃ (𝟎, ∞,)

5. What is the domain and range for the function f(x) = 𝟏 𝒙 ?
QQ:
Write the equation for a quadratic graph that has been stretched by a factor of 3 and shifted up 2.
What is the domain and range for the function
f(x) = 𝟏 𝒙 ?
Which of these is a quadratic function?
f(x) = x(x2 + 1) b) g(x) = x3 – x
c) h(x) = 0x2 – x d) k(x) = x(x -5)

6. Which of these is a quadratic function?
f(x) = x(x2 + 1) b) g(x) = x3 – x
c) h(x) = 0x2 – x d) k(x) = x(x -5)
f(x) = x3 + x
k(x) = x2 – 5x
h(x) = – x

9. Today’s Objective:
I can graph transformed functions from equations and I can create equations of transformed functions from their graphs.

12. Will the winners win?

13. A. 5x2 + 3x +3 B. 18x2 - 18x D. 𝒙 + x -1 C. 9x +2 F. 125x2 E. x2 - 16
Which of these are quadratic equations?
A. 5x x +3
B x x
D. 𝒙 x -1
C. 9x +2
F x2
E. x
G. X3 - x2 + x
H. x(x + 6)

14. Which of these might be the graph of
f(x) = - |x| ? D A B C C

15. What happens to the graph of f(x) = a x2 when a is greater than one?
The graph is stretched; it stays
closer to the y-axis.

16. What is the parent function
of the equation
Y = -3x + 1 ?
Y = x

17. Write the equation for this horizontal translation?
y = |x + 4 |

18. Write the equation of the function that would transform the blue graph into the red graph.
f(x) = -(x -2)2 +2

19. What color is the graph that is a compression of its parent function?
Blue

20. You start with the function: f(x) = |x – 2| + 3 and
move it down 4 units. What is the equation for the new function?
f(x) = |x – 2| -1

21. What is the range of the function
f(x) = 𝒙−𝟑 ?
Range: 0, ∞

22. What happens to the graph of f(x) = a x2 when a is between 0 and 1?
The graph is compressed; it stays
closer to the x-axis; it opens wider.

23. Write an equation for the vertical translation down 4 units of:
y = √x + 3?
y = x -1