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)=(a)/((x-h))+k \\ when\colon h=0,k=0,a=1 \\ f(x)=(1)/(x-0)+0 \\ f(x)=(1)/(x) \\ f(x)=y \\ \Rightarrow y=(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=(1)/(2)=(1)/(2) \\ y=(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=(1)/(-1)=-1 \\ y=-1 \end{gathered}`

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