Question

mary earns $7.25 an hour. she can determine her salary, s, for the number of hours she works, h, by using the equation s = 7.25h. which statement explains why s is a function of h?
a. for every value of h there is only one value of s.
b. for some values of h there is more than one value of s.
c. for some values of s there is more than one value of h.
d. for every value of s there are two values of h.

Explanation:

To determine why \( s \) is a function of \( h \), we recall the definition of a function: a relation where each input (in this case, \( h \)) has exactly one output (in this case, \( s \)). The equation is \( s = 7.25h \), which is a linear equation. For any given number of hours \( h \), multiplying by 7.25 will give exactly one salary \( s \).

• Option A states "For every value of \( h \) there is only one value of \( s \)", which matches the function definition.
• Option B is incorrect because the function definition requires each \( h \) to have only one \( s \), not more.
• Option C and D discuss the reverse (values of \( s \) and corresponding \( h \)), but the question is about \( s \) as a function of \( h \), so we focus on inputs \( h \) and outputs \( s \). Thus, C and D are irrelevant to the function definition in this context.

Answer:

A. For every value of \( h \) there is only one value of \( s \)