Sketch two different examples of functions for each that would satisfy the following

Question

conditions. (i.e. make two different graphs for (a) and two for (b)) a) f06, f32, f41

Answer 1

(a) Two different examples of functions that satisfy the given conditions are:

Example 1:
f(x) = -2x + 6

Example 2:
f(x) = 3x + 6

Here are the graphs for both examples:
Example 1: f(x) = -2x + 6
Graph of Example 1:
(0, 6)
(3, -2)
(-4, 1)

|
6 |
| ●
|
|
0 ----------------------------------------------------
|
-4 ●
|
|
-8

Example 2: f(x) = 3x + 6
Graph of Example 2:
(0, 6)
(3, -2)
(-4, 1)

|
6 | ●
|
|
0 ----------------------------------------------------
|
-4 ●
|
|
-8

(b) Two different examples of functions that satisfy the given conditions are:

Example 1:
f(x) = x^2 - 3x + 6

Example 2:
f(x) = -2x^2 + 4x + 1

Here are the graphs for both examples:
Example 1: f(x) = x^2 - 3x + 6
Graph of Example 1:
(0, 6)
(3, -2)
(-4, 1)

|
6 |
| ●
|
0 ----------------------------------------------------
|
-4 ●
|
|
-8

Example 2: f(x) = -2x^2 + 4x + 1
Graph of Example 2:
(0, 6)
(3, -2)
(-4, 1)

|
6 | ●
|
|
0 ----------------------------------------------------
|
-4 ●
|
|
-8