ANSWER
d.
[tex]f(x) = - \frac{1}{3} |x| [/tex]
EXPLANATION
The parent function is
[tex]f(x)= |x| [/tex]
This function has been reflected in the x-axis and stretched horizontally.
The new equation is in the form:
[tex]f(x)= - a |x| [/tex]
The point, (3,-1) must satisfy this equation,
[tex] - 1 = - a | 3| [/tex]
[tex]3a = 1[/tex]
This implies that,
[tex]a = \frac{1}{3} [/tex]
Hence the correct equation is,
[tex]f(x) = - \frac{1}{3} |x| [/tex]
