f(x)= 3x+2/2x+4

graph the function horizontal and vertical asymptotes. Show the table. I found the horizontal and vertical asymptotes, but im confused on how to do a table

To create a table for a function, you need to select a range of x-values and substitute them into the given function to find the corresponding y-values. Let's create a table for the function f(x) = (3x + 2)/(2x + 4).

To determine the x-values for the table, you can choose any values you prefer. Let's select five x-values: -3, -1, 0, 1, and 3.

Now, we will substitute each x-value into the function to find the corresponding y-values.

1. When x = -3:
f(-3) = (3(-3) + 2)/(2(-3) + 4) = (-7)/(-2) = 7/2 = 3.5

2. When x = -1:
f(-1) = (3(-1) + 2)/(2(-1) + 4) = (-1)/(2) = -1/2 = -0.5

3. When x = 0:
f(0) = (3(0) + 2)/(2(0) + 4) = (2)/(4) = 1/2 = 0.5

4. When x = 1:
f(1) = (3(1) + 2)/(2(1) + 4) = (5)/(6) ≈ 0.833

5. When x = 3:
f(3) = (3(3) + 2)/(2(3) + 4) = (11)/(10) ≈ 1.1

Now we have the x and y values for our function, which we can use to create a table:

```
---------------------
| x | f(x) |
---------------------
| -3 | 3.5 |
| -1 | -0.5 |
| 0 | 0.5 |
| 1 | 0.833 |
| 3 | 1.1 |
---------------------
```

This table shows the x-values and their respective y-values for the function f(x) = (3x + 2)/(2x + 4). You can use this table to plot the points on a graph.

To find the horizontal and vertical asymptotes of the function, you need to analyze the behavior of the function as x approaches positive or negative infinity.

Horizontal Asymptote:
As x approaches positive or negative infinity, the highest power of x in the numerator will dominate the function. In this case, the highest power is x, and the highest power in the denominator is also x. Therefore, the horizontal asymptote is y = 3/2.

Vertical Asymptote:
To find vertical asymptotes, set the denominator equal to zero and solve for x. In this case, the denominator is 2x + 4. Setting it equal to zero gives 2x + 4 = 0, which implies x = -2. Therefore, x = -2 is the vertical asymptote.

By understanding how to create a table for a function and analyzing the behavior of the function as x approaches positive or negative infinity, you can find the horizontal and vertical asymptotes for the given function.