Question

Determine whether the formula describes y as a function of x.

y=−3x²−7x−6
A. Yes, because it is a quadratic function.
B. Yes, because each input value corresponds to exactly one output value.
C. No, because it is not a linear function.
D. No, because it has multiple terms.

Answer 1

The formula y = -3x² - 7x - 6 describes y as a function of x because each input value corresponds to exactly one output value, hence it is a function.

Step-by-step explanation:

The question asks whether the formula y = -3x² - 7x - 6 describes y as a function of x. A function is defined by the condition that each input value (x) corresponds to exactly one output value (y). Considering the definition of a function and the given formula, which is a quadratic function, we can conclude that for every value of x, there is only one corresponding value of y determined by the formula. Therefore, the correct answer is B, Yes, because each input value corresponds to exactly one output value.

Answer 2

Yes because each input value corresponds to exactly one output value.

So. the correct statement is B.

Step-by-step explanation:

The formula y = -3x² - 7x - 6 describes a quadratic function as indicated by the presence of the x² term. Quadratic functions are a type of polynomial function where the highest power of the variable (in this case x) is 2.

In the given quadratic equation each input value of x uniquely determines a single output value of y. This property fulfills the fundamental requirement for a function for every x there exists one and only one corresponding y.

The fact that the function is quadratic means its graph would be a parabola exhibiting a symmetrical U shape. The presence of multiple terms or the nonlinearity of the function does not negate its status as a function.

Each term contributes to the overall value of the function and the function output is solely determined by the input x. The quadratic function model is widely applicable in various fields such as physics and engineering for describing phenomena with quadratic relationships.

So. the correct statement is B.