Master polynomial function analysis, understand degrees, coefficients, end behavior, turning points, and learn comprehensive graphing techniques.
Identify the degree of the polynomial function!
Polynomial Function:
Predict the end behavior based on the leading coefficient and degree!
Polynomial Function:
End Behavior:
A polynomial function is a function of the form:
f(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₁x + a₀
where n is a non-negative integer and aₙ, aₙ₋₁, ..., a₁, a₀ are real numbers.
Key characteristics:
f(x) = 3x³ - 2x² + 5x - 1 ✓ Polynomial (degree 3)
g(x) = x⁴ + 7x² - 3 ✓ Polynomial (degree 4)
h(x) = 1/x + 2 ✗ Not a polynomial (variable in denominator)
k(x) = √x + 3 ✗ Not a polynomial (fractional exponent)
Write f(x) = 5 - 2x + 3x² in standard form:
Step 1: Arrange terms in descending order of degree
Step 2: f(x) = 3x² - 2x + 5
Standard form: Terms written from highest to lowest degree