Evaluate functions using function notation

Evaluating a function in notation means interpreting $f(a)$ as the output associated with input $a$ , then substituting the input into a defining rule and simplifying accurately, including when the input is negative, fractional, or an algebraic expression. The result can be connected to the corresponding value in a table or coordinate on a graph, while respecting domain restrictions and distinguishing $f(a)$ from multiplication. The focus is on standard algebraic functions, not abstract function spaces or advanced limiting techniques.

Detailed Explanation: Evaluate functions using function notation

Function notation tells you which input to use. In $f(a)$ , the number or expression inside the parentheses is the input, and $f(a)$ is the corresponding output. It does not mean $f \times a$ .

To evaluate a function:

Identify the input inside the parentheses.
Substitute that input everywhere the variable appears.
Use parentheses, especially for negative numbers.
Simplify using the order of operations.

Suppose

f(x)=2x^2-3x+1

Find $f(-2)$ .

The input is $-2$ , so replace every $x$ with $(-2)$ :

f(-2)=2(-2)^2-3(-2)+1

Now simplify the exponent and multiplication:

f(-2)=2(4)+6+1

Finally, add:

f(-2)=8+6+1=15

Therefore,

\boxed{f(-2)=15}

This means that the function’s output is $15$ when the input is $-2$ . On a graph, this corresponds to the point $(-2,15)$ .

Learn by doing: Evaluate functions using function notation

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Function Notation - Order One - Function, Find Output

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Evaluate functions using function notation

Detailed Explanation: Evaluate functions using function notation

Learn by doing: Evaluate functions using function notation

Practice with unlimited practice problems

Practice:

Function Notation - Order One - Function, Find Output