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 ࠀࠓࠔࠕࡅࡌࡏ࡙࡜ࡨ࡫ࡷࡺࢉࢌࢍ࣒࣓ऐऑऒगङचजॕॖय़ॡ०१३४६ॳॵািীৈ৊৐৒৓৕ড়৞੺઻ 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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