Question

Which statements about the graph of the function f(x) = 2x2 – x – 6 are true? Check all that apply.
The domain of the function is .


The range of the function is all real numbers.


The vertex of the function is .


The function has two x-intercepts.


The function is increasing over the interval (, ∞

Answer 1

The correct answer for the question that is being presented above is this one: "The range of the function is all real numbers; The function has two x-intercepts. The statements about the graph of the function f(x) = 2x2 – x – 6 that are true includes: The range of the function is all real numbers; The function has two x-intercepts.

Answer 2

we have

$f(x) = 2x^{2} -x-6$

using a graphing tool

see the attached figure

This is a quadratic equation (vertical parabola) open up

The vertex is a minimum---------> Vertex $(0.25,-6.125)$

The domain of the function is all real numbers-------> interval (-∞,∞)

The range of the function is the interval----------> [-6.125,∞)

The function has two x-intercepts-----> $(-1.5,0)$ and $(2,0)$

The function is increasing over the interval-----> (0.25,∞)

The function is decreasing over the interval-----> (-∞,0.25)