identify the equation for this graph. f(x) = x; f(x) = 1/x; f(x) = ln(x); f(x) = x³
identify the equation for this graph. f(x) = x; f(x) = 1/x; f(x) = ln(x); f(x) = x³
Answer
Explanation:
Step1: Analyze the graph shape
The graph shown is a hyperbola with two branches, one in the first quadrant and one in the third quadrant. This is the characteristic shape of a reciprocal function.
Step2: Analyze each option
- For ( f(x)=x ), it is a linear function with a straight line graph passing through the origin with a slope of 1, which does not match the hyperbola shape.
- For ( f(x)=\frac{1}{x} ) (or ( f(x) = 1/x )), the graph of the reciprocal function ( y=\frac{1}{x} ) has two branches in the first and third quadrants (when ( x>0,y>0 ) and ( x < 0,y < 0 )), which matches the given graph.
- For ( f(x)=\ln(x) ), the domain is ( x>0 ) and the graph is only in the first quadrant (for real numbers) and has a different shape, not matching the given graph with two branches.
- For ( f(x)=x^{3} ), it is a cubic function with a graph that passes through the origin and has a different shape (it is a smooth curve passing through the origin and has a single - valued curve for all real ( x )), not matching the hyperbola - like shape of the given graph.
Answer:
B. ( f(x) = 1/x ) (Here we assume the second option is labeled as B, if the original options have labels like A, B, C, D, we follow that. Since the user's options are presented in order, we can say the correct option is the one with ( f(x)=1/x ))