Question

mary earns $7.75 an hour. she can determine her salary, s, for the number of hours she works, h, by using the equation s = 7.75h. 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:

Step1: Recall Function Definition

A function is a relation where each input (independent variable) has exactly one output (dependent variable). Here, \( h \) is the input (hours worked), \( s \) is the output (salary). The equation is \( s = 7.75h \).

Step2: Analyze Each Option

• Option A: For any \( h \), plugging into \( s = 7.75h \) gives one unique \( s \). This matches the function definition.
• Option B: Contradicts the function definition (each \( h \) should have one \( s \)).
• Option C: This talks about \( s \) as input, but the question is why \( s \) is a function of \( h \) (so \( h \) is input). Also, for \( s = 7.75h \), solving for \( h \) gives \( h=\frac{s}{7.75} \), so each \( s \) has one \( h \), not more.
• Option D: Incorrect, as each \( s \) has one \( h \), not two.

Answer:

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