Question

1. f(x) = 5x^2 + 7x-3 Degree:Leading Coefficient:End Behavior:

Answer 1

The degree of the polynomial function f(x) = 5x^2 + 7x - 3 is 2, its leading coefficient is 5, and its end behavior is that f(x) approaches infinity as x approaches both infinity and negative infinity due to its parabolic shape opening upwards.

Step-by-step explanation:

The student is asking about the characteristics of a polynomial function f(x) = 5x^2 + 7x - 3. The degree of this function is 2, since the highest exponent of x is 2. The leading coefficient is 5, as it is the coefficient of the term with the highest exponent. The end behavior of this polynomial is determined by the leading term, 5x^2. As x approaches infinity, f(x) will also approach infinity, and as x approaches negative infinity, f(x) will also approach infinity because the leading coefficient is positive and the degree is even, causing the parabola to open upwards.

Answer 2

f(x) = 5x^2 + 7x-3

The Degree of a polynomial is the highest degree of the polynomial's monomials.

In this case:

Degree: 2

The leading coefficient is the number next to the highest degree variable:

Leading coefficient = 5

End behavior: Degree is even and the leading coefficient is positive, so en behavior is:

f(x) ⇒ ∞ as x ⇒ -∞

f(x)= ∞ as x ⇒ ∞