Posts

How Do You Evaluate a Function? II

\fn_jvn {\color{Blue} f(x)=x^2-2x+4}This post about how to evaluate a function is part of a series of posts to help you prepare for the Advanced Algebra and Functions part of the Accuplacer test.

Question

For the function

\fn_jvn {\color{Blue} f(x)=x^2-2x+4}

what is the value of \inline \fn_jvn f(x-1)?

A.  \inline \fn_jvn x^2-2x+3

B. \inline \fn_jvn (x-1)^2-2(x-1)+4\inline \fn_jvn (x-1)(x^2-2x+3)

C. \inline \fn_jvn (x-1)(x^2-2x+3)

D.  \fn_jvn x^2+3x+4


Solution

f(x-1) is what you get when you replace x with x-1 in . That is called “evaluating the function for x-1.

Sidebar: Function Notation

In algebra, usually when you write two things side by side with one of them in parentheses, that means you multiply those two things together:

\fn_jvn {\color{Blue} a(b)=a \cdot b}

So no one can blame you for thinking f(x) means f multiplied by x. But math notation, like other kinds of language, has exceptions. f(x) means function f, carried out on x. And f(something else) means function f carried out on something else. For example, say function g is defined as . That means ; ; and means  (whatever * means).

It gets interesting when the parentheses in the function definition contain a function. For example, if  , what is ? Well, we said that if you want to find , you insert * into the function definition. To find , insert  into the function definition: if , then .

So to find f(x-1) in the expression

\fn_jvn {\color{Blue} f(x)=x^2-2x+4}

insert x-1 wherever you see x. You should get:

\fn_jvn {\color{Blue} (x-1)^2-2(x-1)+4}

That’s answer choice B.

Usually an answer like this would be expressed as , but this question is multiple choice so you go with what you’ve got.

Another example of how to evaluate a function is here.

This question is similar to question number 13 in the sample questions for the Accuplacer Advanced Algebra and Functions test.