Math

Question Determine if each function is a polynomial: (a) u(x)=9x2x2u(x)=9x-2x^2, (b) f(x)=2+4xf(x)=-2+4\sqrt{x}, (c) v(x)=8v(x)=8, (d) h(x)=4x5+x2/89h(x)=4x^5+x^2/8-9.

Studdy Solution

STEP 1

1. A polynomial function is a function that can be expressed in the form p(x)=anxn+an1xn1++a2x2+a1x+a0p(x) = a_n x^n + a_{n-1} x^{n-1} + \ldots + a_2 x^2 + a_1 x + a_0, where nn is a non-negative integer and the coefficients an,an1,,a0a_n, a_{n-1}, \ldots, a_0 are real numbers.
2. Each term in a polynomial function must have a variable raised to a non-negative integer power.
3. Polynomial functions do not include variables under a radical, variables in the denominator, or variables with negative or fractional exponents.

STEP 2

1. Analyze each function to determine if it meets the criteria for a polynomial function.
2. Mark "Yes" for functions that are polynomial functions and "No" for those that are not.

STEP 3

Analyze the function u(x)=9x2x2u(x)=9x-2x^2 to determine if it is a polynomial function.

STEP 4

Observe that u(x)u(x) consists of terms with variables raised to non-negative integer powers and no variables under radicals or in denominators.

STEP 5

Conclude that u(x)u(x) is a polynomial function and mark "Yes" for function (a).

STEP 6

Analyze the function f(x)=2+4xf(x)=-2+4\sqrt{x} to determine if it is a polynomial function.

STEP 7

Observe that f(x)f(x) includes a variable under a radical, which is equivalent to having a variable with a fractional exponent.

STEP 8

Conclude that f(x)f(x) is not a polynomial function and mark "No" for function (b).

STEP 9

Analyze the function v(x)=8v(x)=8 to determine if it is a polynomial function.

STEP 10

Observe that v(x)v(x) is a constant function, which can be considered as a polynomial of degree 0.

STEP 11

Conclude that v(x)v(x) is a polynomial function and mark "Yes" for function (c).

STEP 12

Analyze the function h(x)=4x5+x289h(x)=4x^5+\frac{x^2}{8}-9 to determine if it is a polynomial function.

STEP 13

Observe that h(x)h(x) consists of terms with variables raised to non-negative integer powers and no variables under radicals or in denominators.

STEP 14

Conclude that h(x)h(x) is a polynomial function and mark "Yes" for function (d).

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord