First, let's define our function: y = x^2 - 2x - 1
Our task is to graph this function and make a table of values where x varies from 0 to 6.
Let's first create our table of values. We'll iterate through each value of x from 0 to 6, and for each value of x, we'll compute the corresponding value of y using our function.
The function is:
- At x = 0; y = (0)^2 - 2*(0) - 1 = -1
- At x = 1; y = (1)^2 - 2*(1) - 1 = -2
- At x = 2; y = (2)^2 - 2*(2) - 1 = -1
- At x = 3; y = (3)^2 - 2*(3) - 1 = 2
- At x = 4; y = (4)^2 - 2*(4) - 1 = 7
- At x = 5; y = (5)^2 - 2*(5) - 1 = 14
- At x = 6; y = (6)^2 - 2*(6) - 1 = 23
So, the table of values is:
| x | y |
|---|----|
| 0 |-1 |
| 1 |-2 |
| 2 |-1 |
| 3 | 2 |
| 4 | 7 |
| 5 | 14 |
| 6 | 23 |
Next, let's graph the function using the values from our table. Start by creating a graph with x-values ranging from 0 to 6 and y-values from -2 to 23. Label the x-axis as 'x' and the y-axis as 'y'. At each (x, y) point from our table of values, plot a point on our graph (remember that each point corresponds to (x, y)). Connect these points to form the graph of function.
The graph of the function y = x^2 - 2x - 1 between x=0 and x=6 will be a curve that opens upwards, starting at y=-1 for x=0, then going down to y=-2 for x=1, then going up again to y=-1 for x=2 and continuously increasing until reaching the point (6, 23).
Finally, add a title to the graph: "Graph of function y = x^2 - 2x - 1"
And this is how you graph the function y = x^2 - 2x - 1 and create a table of its values.