Question

question 4 of 5
select the correct answer.
if h is a function and -7 is an element in its domain, then which of the following statements correctly describes the expression h(-7)?
the expression h(-7) represents that -7 is the only element in the domain of h.
the expression h(-7) represents the input of h corresponding to the output of -7.
the expression h(-7) represents the output of h corresponding to the input of -7.
the value of h should be multiplied by -7 to evaluate the expression.

Explanation:

To determine the correct description of \( h(-7) \) for a function \( h \) where \(-7\) is in the domain:

• Recall the definition of a function: For a function \( h \), \( h(x) \) represents the output (or range value) corresponding to the input \( x \) (which is in the domain).
• Analyze each option:
• "The expression \( h(-7) \) represents that \(-7\) is the only element in the domain of \( h \)." → Incorrect. Just because \(-7\) is in the domain doesn't mean it's the only element.
• "The expression \( h(-7) \) represents the input of \( h \) corresponding to the output of \(-7\)." → Incorrect. The input is \(-7\), and \( h(-7) \) is the output for that input, not the other way around.
• "The expression \( h(-7) \) represents the output of \( h \) corresponding to the input of \(-7\)." → Correct. By the definition of function notation, \( h(x) \) gives the output when \( x \) is the input. Here, \( x = -7 \), so \( h(-7) \) is the output for input \(-7\).
• "The value of \( h \) should be multiplied by \(-7\) to evaluate the expression." → Incorrect. Function notation \( h(-7) \) means we evaluate the function \( h \) at \( x = -7 \), not multiply \( h \) by \(-7\).

Answer:

The expression \( h(-7) \) represents the output of \( h \) corresponding to the input of \(-7\).