Algebra / Linear Functions

Linear Function Notation and Inputs

Function notation describes input-output relationships. Linear function questions often ask for a function value, an input that gives a specified output, a rate of change, or a parameter in a function rule.

Least you need to know

$f(a)$ means substitute $a$ for the input variable.
To solve $f(x)=c$, set the expression for $f(x)$ equal to $c$ and solve for $x$.
For $f(x)=mx+b$, $m$ is the rate of change and $b=f(0)$.
A transformed input such as $f(x+h)$ changes the value substituted into the function.

Key notation

$f(3)$ — The output of function $f$ when the input is 3
$f(x)=2x+7$ — A linear function with rate of change 2 and initial value 7

Worked example

If $f(x)=4x-5$, then $f(6)=4(6)-5=19$.
If $f(x)=19$, then $4x-5=19$, so $x=6$.

Common mistakes

Do not confuse the input with the output.
When evaluating $f(x+2)$, substitute the entire expression $x+2$ for the input.
A table may not include $x=0$, so the initial value may need to be calculated.

How to recognize it

The problem uses notation such as $f(a)$, $f(x)=c$, or $f(x+h)$.
The problem asks for an input or an output.
The function is linear or represented by a table.

下一節推薦課程

通過 Linear Function Tables, Rates, and Models 繼續學習此主題。

Linear Function Tables, Rates, and Models