Question

graph the function. be sure to label three points on the graph.

$f(x)=\frac{1}{x}$

choose the correct graph.

a.
b.
c.
d.

Explanation:

Step1: Find points on the function

For \(f(x)=\frac{1}{x}\), when \(x = 1\), \(y=f(1)=\frac{1}{1}=1\). So the point is \((1,1)\).
When \(x=- 1\), \(y = f(-1)=\frac{1}{-1}=-1\). So the point is \((-1,-1)\).
When \(x = 2\), \(y=f(2)=\frac{1}{2}\). So the point is \((2,\frac{1}{2})\).
When \(x=-2\), \(y = f(-2)=\frac{1}{-2}=-\frac{1}{2}\). So the point is \((-2,-\frac{1}{2})\).

Step2: Analyze the function's properties

The function \(y = \frac{1}{x}\) is a hyperbola. Its domain is \(x
eq0\) and range is \(y
eq0\). It is symmetric about the origin. That is, if \((x,y)\) is on the graph, then \((-x,-y)\) is also on the graph.

Answer:

Assuming that option B has the points \((1,1)\), \((-1, - 1)\) and other points consistent with \(y=\frac{1}{x}\) (since the actual visual of graphs A - D is limited in text - only context but based on the function \(y = \frac{1}{x}\)'s properties), the answer is B.