COMPARING LINEAR, QUADRATIC AND EXPONENTIAL FUNCTIONS



COMPARING FUNCTIONS

|Name of Function |Table of Values |Sketch |

|Linear | | |

| | |[pic] |

|Quadratic | |[pic] |

|Exponential | |[pic] |

| | | |

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 | |x |Y | |

|-4 |5 | |-5 |32 | |

|-3 |8 | |-4 |16 | |

|-2 |13 | |-3 |8 | |

|-1 |20 | |-2 |4 | |

|0 |29 | |-1 |2 | |

|1 |40 | |0 |1 | |

|x |y | |x |y | |

|-2 |-2.75 | |0.5 |0.9 | |

|0 |-2 | |0.75 |1.1 | |

|2 |1 | |1 |1.3 | |

|4 |13 | |1.25 |1.5 | |

|6 |61 | |1.5 |1.7 | |

|8 |253 | |1.75 |1.9 | |

Identify the following equations as linear, quadratic or exponential.

|1. [pic] |2. [pic] |

|3. [pic] |4. [pic] |

|5. [pic] |6. [pic] |

All Linear functions have _______________________.

All Quadratic functions have a _____________________________.

All Exponential 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.

Looking at the graphs:

a) Which function shows a constant rate of change in its y values?

How is this displayed on your graph?

b) Eventually, which type of function shows the most rapid rate of growth in its y values?

How is this displayed on your graph?

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 5. y = 3x +3 6. [pic]

7. Summarize the differences between y = 3x and y = 5x for x values [pic] by creating tables of values and graphing each on the same grid. Use a chart to summarize:

(a) symmetry

(b) any x- and y- intercepts

(c) when the y-values are increasing

(d) when the y-values are decreasing

(e) what happens to the y-values as x gets larger in the positive direction

(f) what happens to the y-values as x gets larger in the negative direction.

2. Will the graph of y = 2x ever touch the x-axis? Explain.

3. In the relations y = x2 and y = 2x, are the y-values ever negative? Explain.

-----------------------

This function is. rð ðlinear rð quadratic rð exponential

What methods can you use to verify the type of function selected?

This function is. rð linear rð quadratic rð exponential

How do you know?

What do the 1st and 2nd differences represent is 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 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

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download