Use the function to evaluate the indicated expressions and simplify. f(x)=6 x-18 ; f((x)/(3)),

Use the function to evaluate the indicated expressions and...

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Key Concepts

Linear Functions

Linear functions are functions of the form ax + b, where a and b are constants. They are characterized by a constant rate of change, and their graphs form straight lines, making them one of the simplest types of functions.

Algebraic Simplification

Algebraic simplification involves combining like terms, performing arithmetic operations, and reducing expressions to their simplest form. This skill is crucial for making complex expressions more understandable and manageable.

Function Evaluation

This concept involves replacing the variable in a function with a specific value or expression and then simplifying the resulting expression to determine the function's output. It is fundamental to understanding how functions work in mathematics.

Substitution

Substitution is the process of inserting another expression into a function in place of the variable. It is an essential skill for transforming and evaluating expressions within functions by altering their inputs.

Transcript

00:02 Welcome everybody.

00:04 Today we are given a function and the two expressions to simplify.

00:09 Our function is f of x equal to 6x minus 18.

00:17 Given this function, can you give me the simplest expression of f of x over 3, also f of x, the whole thing divided by 3? before we begin, let's just remind everybody, a function really is a set of rules that turn a specific object taken in, let's say, next, run it through a bunch of operations, and give out a new object.

00:49 So in this case, the set of rules that we have to follow for our object given is 6x minus 18.

00:56 So this is really saying given x, multiply that x by 6, subtract 18.

01:02 And that would be our outcome of this function.

01:07 So with that in mind, let's just write out what f of x3 look like.

01:13 So whatever there is the x written up here in the definition of function, you're just going to plug in x number three.

01:20 So six times x number three minus 18.

01:27 So now after it's written out like this, you really just have to simplify it everything to clay.

01:33 So six on top, three in the bottom.

01:36 Is there any number i can choose to divide both of them so we can produce a little cleaner number.

01:41 I think number three will do in this case.

01:44 Three divided by three is one...

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