Question

Evaluate f(×) for the given value for x. I will send the image

Answer 1

To answer this question, we need to substitute the value of x into the given "rule" for the function as follows:

`f(x)=x^2+6\Rightarrow f(-2)=(-2)^2+6\Rightarrow f(-2)=4+6`

Therefore, we have:

`f(-2)=10`

Therefore, the ordered pairs (x, f(x)) are (-2, 10).

We can graph this point on the graph as follows:

Then, if we have other values for x, such as x = -1, x = 0, x = 1, and x = 2, we can follow the same steps as before for each value of x. Then, we need to evaluate the function for each value of x as follows:

x = -1

`f(-1)=(-1)^2+6=1+6\Rightarrow f(-1)=7`

x = 0

`f(0)=(0)^2+6\Rightarrow f(0)=6`

x = 1

`f(1)=(1)^2+6=1+6\Rightarrow f(1)=7`

x = 2

`f(2)=(2)^2+6=4+6\Rightarrow f(2)=10`

Now, to graph the function, we have the other ordered pairs as follows: (-1, 7), (0, 6), (1, 7), (2, 10).

Then, we can graph those points as follows:

As we can see, this is the graph of a parabola, with vertex (0, 6).

We can see more clearly if we use a graphing calculator as follows:

In summary, to graph the function, we need to evaluate the function for each value of x following the "rule" of the function, in this case we have: