Question

which are cubic functions? check all that apply.\\( f(x) = -4 - 2x + 5x^3 \\)\\( f(x) = -3^x - 1 \\)\\( f(x) = -x^2 + 5x - x^3 \\)\\( f(x) = x^2 - 6x^3 + 2x^4 + 1 \\)\\( f(x) = 2x^3 + 3x^2 - x - 3 \\)\\( f(x) = 3x^2 - 1 - 8x \\)

Explanation:

A cubic function is a polynomial function of degree 3, meaning the highest power of \( x \) is 3. Let's analyze each function:

1. \( f(x) = -4 - 2x + 5x^3 \): The highest power of \( x \) is 3 (from \( 5x^3 \)), so it is a cubic function.
2. \( f(x) = -3^x - 1 \): This is an exponential function (with base 3), not a polynomial, so not cubic.
3. \( f(x) = -x^2 + 5x - x^3 \): The highest power of \( x \) is 3 (from \( -x^3 \)), so it is a cubic function.
4. \( f(x) = x^2 - 6x^3 + 2x^4 + 1 \): The highest power of \( x \) is 4 (from \( 2x^4 \)), so it is a quartic (degree 4) function, not cubic.
5. \( f(x) = 2x^3 + 3x^2 - x - 3 \): The highest power of \( x \) is 3 (from \( 2x^3 \)), so it is a cubic function.
6. \( f(x) = 3x^2 - 1 - 8x \): The highest power of \( x \) is 2, so it is a quadratic (degree 2) function, not cubic.

Answer:

• \( f(x) = -4 - 2x + 5x^3 \)
• \( f(x) = -x^2 + 5x - x^3 \)
• \( f(x) = 2x^3 + 3x^2 - x - 3 \)