Are these Linear Functions notes free?

Yes. The full 3-page Linear Functions sheet is free inside CapCompass, which runs in your browser with no account needed.

What does the Linear Functions revision sheet cover?

Function notation, stripped down, the shape of every linear function, f(a) means, slope from two outputs, one step along x, n steps along x, Nonzero slope vs zero slope, m is not 0, m = 0, What the two numbers mean in a real model, Two pictures of the same idea, Four questions, four instant moves.

Is this for Digital SAT SAT Math?

Yes, it is written for the Digital SAT SAT Math syllabus.

🧭 CapCompassfree study planner

Linear Functions — Digital SAT SAT Math revision notes

A 3-page visual revision sheet for Linear Functions, written for Digital SAT SAT Math. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.

Linear Functions revision notes, page 1 of 3 — A preview of page 1 — all 3 pages open full size in the app.

Linear Functions in one look

one rate, one starting value, and a graph that never changes its mind

Function notation, stripped down

the shape of every linear function f(x) = mx + b
f(a) means put a in place of x
slope from two outputs m = f(x_2) - f(x_1)/x_2 - x_1
one step along x f(x+1) - f(x) = m
n steps along x f(x+n) - f(x) = mn

Q. The function g is defined by g(x) = 1/2x - 4. If g(k) = 6, what is k?

g(k) means substitute k for x: 1/2k - 4 = 6
add 4 to both sides: 1/2k = 10
multiply both sides by 2

Answer: k = 20

Nonzero slope vs zero slope

m is not 0

the output changes at a steady rate
the graph crosses the horizontal axis exactly once
there is exactly one x with f(x) = 0

m = 0

f(x) = b for every input, a constant function
the graph is a flat horizontal line
no x makes f(x) = 0 unless b is already 0

Page 1 of 3. The full sheet, all 3 pages, opens free in the app.

What this Linear Functions sheet covers

Function notation, stripped down
the shape of every linear function
f(a) means
slope from two outputs
one step along x
n steps along x
Nonzero slope vs zero slope
m is not 0
m = 0
What the two numbers mean in a real model
Two pictures of the same idea
Four questions, four instant moves
What does this number mean
Find f(a)
Find x when f(x) = c
Write the function
Traps that cost points
Tricks that save time

Open the full Linear Functions sheet →Free, works offline, no account needed. All 3 pages, plus a study plan built around your own exam dates.

How CapCompass uses this sheet

These notes are not a standalone PDF. CapCompass plans SAT Math chapter by chapter against your real exam dates and free hours, and when the plan reaches Linear Functions the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.