Find the indicated function values. f(x)=(-x)^3-x^2-x+10 a. f(0) b. f(2) c. f(-2) d. f(1)+f(-1)

Name: Problem 18, Chapter 8: Introductory and Intermediate Algebra for College Students 4th
Uploaded: 2020-06-28T21:31:02-08:00
Duration: 4 min 45 s
Channel: Sheila Akinleye
Description: Find the indicated function values. f(x)=(-x)^3-x^2-x+10 a. f(0) b. f(2) c. f(-2) d. f(1)+f(-1)

Find the indicated function values. f(x)=(-x)^3-x^2-x+10 a....

Key Concepts

Arithmetic Operations

Arithmetic operations such as exponentiation, multiplication, addition, and subtraction are fundamental when evaluating functions. Correctly applying the order of operations ensures that the evaluation of expressions, especially polynomials, is performed accurately.

Substitution

Substitution involves replacing the variable in an algebraic expression or function with a specific value. This basic mathematical tool is crucial for computing function values and is utilized frequently when dealing with polynomial expressions.

Function Evaluation

Function evaluation is the process of substituting a given number into a function's variable(s) to compute the output. It requires an understanding of the function's definition and careful replacement of the variable in order to obtain the correct result.

Polynomial Functions

Polynomial functions are algebraic expressions that consist of terms involving non-negative integer powers of a variable. They are common in algebra and calculus and are typically evaluated by substituting specific values for the variable and applying arithmetic operations accordingly.

Transcript

00:02 Okay, the question that we have is f of x, our function is equal to negative x raised to the fifth power minus x to the second power minus x plus eight.

00:18 And we want to find this function for a few different values of x, f of zero, f of three, f of negative three, and f of two.

00:36 Plus f of negative 2.

00:38 All right.

00:42 And the space down here in the last two lines will reserve for that last part.

00:46 So what we're doing simply is making a substitution.

00:49 We'll have zero.

00:51 And i should have put, there is a negative sign here, right there.

00:55 And that negative sign is going to be really important because we'll have to make sure that we keep that as part of our function.

01:02 So i have negative zero raise to the fifth power, minus zero raise the fifth second power, minus zero plus eight is equal to eight, because everything else becomes zero.

01:17 Now with three, remember we have that negative sign there.

01:20 We'll put in positive three next to the negative, which makes it a negative three to the fifth power, minus three to the second power, minus three plus eight.

01:31 That's going to be a negative 243, minus nine.

01:38 Minus 3 plus 8.

01:41 Now we do need to have a calculator handy in order to do these.

01:44 Negative 243 minus 9 minus 3 plus 8 gives us negative 247.

01:52 Now with the negative we have a negative that was in the function and now the number we're substituting in is negative.

02:01 So negative of a negative 3 raise to the fifth power minus negative three raised to the second power minus negative three plus eight.

02:16 What does all this come out to be? well, negative of a negative is positive.

02:20 So positive three raised to the fifth power is positive 243...