Verified answer

The domain is all values of x you can plug in that won't give you an undefined answer. Since there is no denominator, you can plug in any value of x without a problem, meaning that all values of x from negative to positive infinity will work.

Therefore, the domain is (-infinity, + infinity)

The range is all values of y. This is a bit more complicated.

This is a quadratic equation, with the general formula ax^2 + bx + c = 0. a determines if the graph goes up or down. Since it is negative, the curve goes downward. Since it is a squared function (to the second power) it will go down forever to negative infinity. Now, we just need to find the maximum point and we'll have the range. For the x-value, there is a formula -b/2a. In this instance, using the equation f(x) = -7x^2 - 11x + 9 , a = -7, b = -11, and c = 9. -b/2a = -(-11)/(2*-7), which is -11/14. This means that at an x value of -11/14 we have our maximum value of y.

To find the y value at this point, we simply plug it into our equation as x..

f(-11/14) = (-7*(-11/14)^2) - 11(-11/14) + 9

This is a bit messy, and with a number like -11/14 i'd recommend just putting it into a calculator.

However, the y value comes out to be 13.321.

As the range is just the y values, going from minimum to max, our range is (-infinity, 13.321)

To sum it up..

domain = (-infinity,+infinity)

range = (-infinity, 13.321)

Hope this helps, sorry if it was a bit confusing!

F(x)=-7(x+11/14)^2+1936/196

domain is infinitife

range is -infinty,1936/196

this function is defined every where on number line so its Domain is R and range is also R, where R denotes the set of real numbers.