Question

The graph shows the reciprocal parent function.Which statement best describes the function?O A. The function is negative when x < 0.OB. The function is never negative.C. The function is negative when x > 0.O D. The function is negative when x < 0 and also when x > 0.PREVIOUS

Answer 1

Let's begin by identifying key information given to us in the graph:

The reciprocal parent function is given as 1/f(x). This is better written as shown below

$\begin{gathered} f(x)=\frac{a}{(x-h)}+k \\ when\colon h=0,k=0,a=1 \\ f(x)=\frac{1}{x-0}+0 \\ f(x)=\frac{1}{x} \\ f(x)=y \\ \Rightarrow y=\frac{1}{x} \end{gathered}$

When the value for x is greater than zero, the function is positive as shown below:

$\begin{gathered} x=2 \\ y=\frac{1}{2}=\frac{1}{2} \\ y=\frac{1}{2} \end{gathered}$

When the value of x is lesser than zero, the function is negative as shown below:

$\begin{gathered} x=-1 \\ y=\frac{1}{-1}=-1 \\ y=-1 \end{gathered}$

Therefore, the correct answer is option A (The function is negative when x < 0)