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.
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