Unit 1 · Core unit
Function notation, domain and range, and the transformations that move any graph. Learned once, this unit applies to every family that follows.
What a strong answer looks like
A strong answer applies inside changes in the opposite direction to their sign, and states domain restrictions explicitly.
Know
Function notation names an output for an input. Division, even roots, and logarithms each remove values from a domain.
Apply
Find a domain by excluding what breaks the expression, then read the range from the resulting shape.
Watch out
Treating function notation as multiplication.
Study move
State the domain of a rational, a radical, and a logarithmic expression.
Know
Changes inside the function act horizontally and opposite to their sign; changes outside act vertically as written.
Apply
Decompose into steps and apply them to a known point, working inside changes backwards.
Watch out
Reading a horizontal compression as a stretch, or a shift in the wrong direction.
Study move
Track one point through a transformation with a reflection, a compression, and two shifts.
Know
Composition feeds one output into another function, and the domain inherits both restrictions. An inverse exists only where a function is one-to-one.
Apply
Find an inverse by exchanging input and output roles and solving; restrict the domain first if needed.
Watch out
Claiming an inverse exists for a function that fails the horizontal line test.
Study move
Find the domain of a composition where the inner function restricts the outer.
Modeling drill
Given a point on a graph, find the corresponding point after a reflection, a horizontal compression, and a vertical shift.
