Algebra / Linear Functions
Linear Functions
A linear function has a constant rate of change and can often be written as $f(x)=mx+b$, where $m$ is the rate of change and $b$ is the value of the function when $x=0$.
Least you need to know
- The rate of change of a linear function is constant.
- The slope between two points is change in output divided by change in input.
Key notation
- $f(x)$ — The output of function $f$ for input $x$
Worked example
- Use two function values to find the rate of change.
- Substitute one point to find the initial value.
Common mistakes
- Function notation asks for an output, not multiplication.
- The initial value is the output when the input is 0.
How to recognize it
- The problem mentions slope, rate of change, initial value, or function notation.
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