Let's analyze each of the given functions in turn to determine whether they are power or polynomial functions and identify their respective power or degree.
1. Function [tex]\( f(x) = -3\sqrt{x} \)[/tex]
- Classification: This is a power function.
- Power: The square root of [tex]\( x \)[/tex] can be expressed as [tex]\( x^{1/2} \)[/tex]. Therefore, the power of this function is [tex]\( 0.5 \)[/tex].
2. Function [tex]\( f(x) = 2(3x-5)^4 \)[/tex]
- Classification: This is a polynomial function in the form [tex]\((3x-5)\)[/tex] raised to the power of 4, which makes it a polynomial term.
- Degree: The degree of the polynomial is determined by the highest power of [tex]\( x \)[/tex], which in this case is 4.
3. Function [tex]\( f(x) = 5x - 3x^3 + x^2 \)[/tex]
- Classification: This is a polynomial function.
- Degree: To find the degree of this polynomial, look at the highest power of [tex]\( x \)[/tex] present in the terms. The terms are [tex]\( 5x \)[/tex], [tex]\( -3x^3 \)[/tex], and [tex]\( x^2 \)[/tex]. The highest power is 3, so the degree of the polynomial is 3.
Now, let's organize the information clearly:
1. Function: [tex]\( f(x) = -3\sqrt{x} \)[/tex]
- Power or Polynomial: Power
- Power or Degree: [tex]\( 0.5 \)[/tex]
2. Function: [tex]\( f(x) = 2(3x-5)^4 \)[/tex]
- Power or Polynomial: Polynomial
- Power or Degree: [tex]\( 4 \)[/tex]
3. Function: [tex]\( f(x) = 5x - 3x^3 + x^2 \)[/tex]
- Power or Polynomial: Polynomial
- Power or Degree: [tex]\( 3 \)[/tex]
This is the complete analysis and classification for each of the given functions.
