Question

Graph the function, give the domain and the rangey=x^2+14x+6

Answer 1

To graph the function given we need to find some points that passes through the graph; to find them we give values to x and then use the equation to find the corresponding value of y, this will given a point on the graph. For example, if x=-9 we have:

`\begin{gathered} y=(-9)^2+14(-9)+6 \\ y=81-126+6 \\ y=-39 \end{gathered}`

hence the graph of the function passes through the point (-9,39). Given more values to x we get a table of the form:

Once we have a few points we plot them on the plane:

Finally, we join the points with a smooth curve to get the graph of the function. Therefore, the graph is:

From the graph we notice that the domain of the function are all the real numbers, this comes from the fact that the function uses all the values of x available. On the other hand, the values of y start from -43 and goes to inifinity.

Therefore:

`\begin{gathered} domain=(-\infty,\infty) \\ range=\lbrack43,\infty) \end{gathered}`