Question

Which best describes the end behavior of y=7x^2?

As x > 0 increases, f(x) decreases. As x < 0 decreases, f(x) decreases.

As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) decreases.

As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) increases.

As x > 0 increases, f(x) decreases. As x < 0 decreases, f(x) increases.

Answer 1

As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) increases.
because f(x) is a quadratic with lowest point at x=0

Answer 2

Option C is correct.

as x > 0 increases, f(x) increases,

as x < 0 decreases, f(x) increase.

Explanation:

Given the function:
`y = 7x^2`

Degree of the polynomial states that the sum of the exponents of each variable in the expression.

The degree of
`7x^2` is 2 i.e Even

The leading coefficient of the polynomial
`7x^2` is, 7 i.e, Positive.

End behavior of the polynomial is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

Also, the degree and the leading coefficient of a polynomial function determine the end behavior of the graph.

Since, the degree of the given function is even and the leading coefficient is positive.

End behavior of the function
`y = 7x^2` is:

as
`x \rightarrow +\infty`, then
`f(x) \rightarrow +\infty`

and

as
`x \rightarrow -\infty` , then
`f(x) \rightarrow +\infty`

Therefore, as x > 0 increases, f(x) increases.

As x < 0 decreases, f(x) increases.