Arithmetic combinations of functions

Arithmetic combinations of functions

Practise adding, subtracting, multiplying and dividing functions while keeping track of the inputs on which each operation is defined. The emphasis is pointwise combination: both original functions receive the same input before their outputs are combined.

This set connects table values, algebraic rules and a pair of coordinate graphs. Domain problems include declared interval restrictions, square roots and a denominator that vanishes inside a common domain. Worked explanations show why simplification can shorten a formula without restoring an input excluded by the original definition.

Contextual questions interpret profit as a difference and average cost as a quotient, including the units and feasible inputs of each quantity. Conceptual items distinguish subtraction order from the commutative operations and examine what happens when two functions have no shared real input.

Review function evaluation, factoring, real square roots and interval notation before starting. Write the common domain first, then add any denominator restriction. Single-select and multiselect items move from direct evaluation to interpretation and error analysis. This is focused topic practice; composition, in which one function receives another function's output, is developed in the next set.