Question

1 state how the graph of the equation will differ from the parent graph \\(\frac{1}{x}\\).
\\(f(x) = -5 + \frac{1}{x}\\)
the graph will shift up 5 units from its parent graph.
the graph will shift left 5 units from its parent graph.
the graph will shift right 5 units from its parent graph.
the graph will shift down 5 units from its parent graph.

Explanation:

Step1: Recall Vertical Shift Rule

For a function \( y = f(x)+k \), if \( k>0 \), shift up \( k \) units; if \( k<0 \), shift down \( |k| \) units.
The parent function is \( y=\frac{1}{x} \), and the given function is \( f(x)=-5 + \frac{1}{x}=\frac{1}{x}-5 \). Here, \( k = - 5 \), so \( |k| = 5 \) and \( k<0 \).

Step2: Determine the Shift

Since \( k=-5<0 \), the graph of \( f(x) \) shifts down 5 units from the parent graph \( y = \frac{1}{x} \).

Answer:

The graph will shift down 5 units from its parent graph.