COMPARING LINEAR, QUADRATIC AND EXPONENTIAL …
COMPARING FUNCTIONS
|Name of Function |General Shape of Graph |Sketch |
|Linear | | |
|Quadratic | | |
|Exponential | | |
|Square Root | | |
|Absolute Value | | |
1. Complete the following tables and answer the questions to the right.
(a)
| X |y = 2x |1st Diff |
| -3 | | |
| -2 | | |
| -1 | | |
| 0 | | |
| 1 | | |
| 2 | | |
| 3 | | |
(b)
| x | y = x2 |1st Diff |2nd Diff |
| -3 | | | |
| -2 | | | |
| -1 | | | |
| 0 | | | |
| 1 | | | |
| 2 | | | |
| 3 | | | |
(c)
| x | y = 2x |1st Diff |2nd Diff |
| -3 | | | |
| -2 | | | |
| -1 | | | |
| 0 | | | |
| 1 | | | |
| 2 | | | |
| 3 | | | |
2. Use differences to identify the type of function represented by the table of values. Then label which type of function each table of values models.
|x |y |
|3. [pic] |4. [pic] |
|ρ linear ρ quadratic ρ exponential |ρ linear ρ quadratic ρ exponential |
|5. [pic] ρlinear ρ quadratic ρ exponential |6. [pic] ρlinear ρ quadratic ρ exponential |
All _______________ functions have _______________________.
All _______________ functions have a _____________________________.
All _______________ functions must have a _______________ in the _______________.
Graph the functions y = 2x, y = x2 and y = 2x on the same grid for [pic]. Label your graphs.
[pic]
Looking at the graphs above:
a) Which function shows a constant rate of change in its y values?
How is this displayed on your graph?
b) For [pic] which function shows the fastest rate of change in its y values?
How is this displayed on your graph?
c) Eventually, which type of function shows the most rapid rate of growth in its y values?
How is this displayed on your graph?
Name: ________________________________ April 25
Practice Problems
Identify the following equations as linear, quadratic or exponential.
1. y = 4x + 6 2. [pic]
3. y = [pic] 4. y = -2(4)x
[pic]
5. y = 3x +3 6. [pic]
Name: ________________________________ April 25
Practice Problems
Identify the following equations as linear, quadratic or exponential.
1. y = 4x + 6 2. [pic]
3. y = [pic] 4. y = -2(4)x
[pic]
5. y = 3x +3 6. [pic]
Name: ________________________________ April 25
Practice Problems
Identify the following equations as linear, quadratic or exponential.
1. y = 4x + 6 2. [pic]
3. y = [pic] 4. y = -2(4)x
[pic]
5. y = 3x +3 6. [pic]
-----------------------
This function is. ρ linear ρ quadratic ρ exponential
What methods can you use to verify the type of function selected?
This function is. ρ linear ࠀࠓࠔࠕࡅࡌࡏ࡙ࡨࡷࡺࢉࢌࢍ࣒࣓ऐऑऒगङचजॕॖय़ॡ०१३४६ॳॵািীৈড় ρ quadratic ρ exponential
How do you know?
What do the 1st and 2nd differences represent in this function?
What do you notice about the differences in this function?
______________________________________________
By what number is the first difference multiplied by to get the next term in the sequence of y-values? ______________________________________________
How does this value connect to the function?
______________________________________________
This function is. ρ linear ρ quadratic ρ exponential
What methods can you use to verify the type of function selected?
This is called an _________________ function
y
40
30
20
10
x
0 1 2 3 4 5
................
................
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