Question

Determine the domain and range of the function f(x)=3x^2+6x-2

Answer 1

Domain: (−∞,∞),x∈R

Range: [−5,∞),y

Explanation:

Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.

Vertex: (-1,-5)

y-intercept(s): (0,−2)

Answer 2

The domain of the function are all values that you can input, in the graphic, they are all values in the x-axis where the function is defined.

The domain for this kind of function is all real numbers, any real number you imput in the function will generate a valid output.

x∈R.

The range of the variable id determined by all output values, i.e. the values shown in the y-axis. In this case as you see, the function decreases until point (-1,-5), then it stats increasing again towards +∞

There are no outputs defined for this varieble below y=-5 so the range of the variable is all real numbers equal or greater than -5

y≥-5

y∈R