Question

question 10 of 22
is the following graph a linear function, a nonlinear function, and/or a
relation?
graph
a. nonlinear function, but not a relation
b. linear function, but not a relation
c. linear function and a relation
d. nonlinear function and a relation

Explanation:

1. Relation Check: A relation is any set of ordered pairs \((x,y)\), and a graph represents a relation (as it shows pairs of \(x\) and \(y\) values). So the graph is a relation.
2. Function Type Check: A linear function has a straight - line graph (represented by \(y = mx + b\), where \(m\) and \(b\) are constants). The given graph is curved (not a straight line), so it is a nonlinear function.
3. Option Elimination:

• Option A is wrong because all functions (and this is a function, as it passes the vertical line test) are relations.
• Option B is wrong because the graph is not a straight line (so not linear) and all functions are relations.
• Option C is wrong because the graph is curved (not linear).
• Option D is correct as the graph is a nonlinear function (curved) and also a relation (since it represents ordered pairs \((x,y)\)).

Answer:

D. Nonlinear function and a relation