Which best describes manipulation of functions?

• A. Altering a function's equation or graph through transformations or algebraic manipulations
• B. Only adding constants
• C. Only multiplying by scalars
• D. Changing the function's domain only

Answer: (A)

Manipulation of functions means changing a function in a way that gives another function, either by altering its defining equation or by adjusting its graph. This includes transformations such as shifts, stretches, and reflections, as well as algebraic changes to the expression that defines the function—like composing with another function, simplifying, or solving for a variable. So the idea is broad: you’re modifying the function itself through both changes to its formula and changes to its graph.

This is why the description that mentions altering the function’s equation or graph through transformations or algebraic manipulations is the best fit. It covers shifts, scales, reflections, and other edits to the formula, not just a single type of change. Simply adding constants, or only multiplying by scalars, are narrower cases that don’t encompass all the ways a function can be manipulated. Changing the domain alone focuses on where the function is defined rather than how the function itself is transformed or expressed.