Make a table with the domain of {2,3,4,5,6} and draw a graph of the absolute value function y = 2|x-4| + 3.
just calculate the values in the y column. For example,
2|3-4|+3 = 2*|-1|+3 = 2*1+3 = 2+3 = 5
now do the same steps for the other values.
Then plot the points and connect the dots...
The thing I am confused on is how do i made a table with the domain and do I use the function given to me to put the table/numbers into?
Oh okay, Thank you Oobleck I will try that. (I sent my comment before I saw yours, my bad)
the table usually consists or two rows (or columns)
One row contains the values in the domain (the ones they gave you)
the other is calculated from those values.
and yes, you use the function they gave you to calculate the values in the range (the other row)
To create a table with the given domain and the absolute value function y = 2|x-4| + 3, you need to substitute each value from the given domain into the function and calculate the corresponding y value.
Here's how you can do it step by step:
Step 1: Write down the given domain: {2, 3, 4, 5, 6}
Step 2: Substitute each value from the domain into the function and calculate the corresponding y value.
For x = 2:
y = 2|2-4| + 3
y = 2|-2| + 3
y = 2(2) + 3
y = 4 + 3
y = 7
For x = 3:
y = 2|3-4| + 3
y = 2|-1| + 3
y = 2(1) + 3
y = 2 + 3
y = 5
For x = 4:
y = 2|4-4| + 3
y = 2|0| + 3
y = 2(0) + 3
y = 0 + 3
y = 3
For x = 5:
y = 2|5-4| + 3
y = 2|1| + 3
y = 2(1) + 3
y = 2 + 3
y = 5
For x = 6:
y = 2|6-4| + 3
y = 2|2| + 3
y = 2(2) + 3
y = 4 + 3
y = 7
Step 3: Create a table with the values of x and corresponding y:
```
| x | y |
|-------|-------|
| 2 | 7 |
| 3 | 5 |
| 4 | 3 |
| 5 | 5 |
| 6 | 7 |
```
To draw the graph of the absolute value function y = 2|x-4| + 3, plot each point from the table on a coordinate plane and connect the points with a smooth curve.
The graph will have a "V" shape with the vertex at (4, 3) and open upwards. The branches of the "V" will extend towards positive infinity for values greater than 4 and will extend towards negative infinity for values less than 4.