Question

identify the equation for this graph. f(x) = x; f(x) = |x|; f(x) = 1/x; f(x) = √(x)

Explanation:

Step1: Analyze the graph's shape

The graph is a straight line passing through the origin, with a slope of 1, existing in all four quadrants (positive and negative x and y values).

Step2: Match to function options

• $f(x)=|x|$ forms a V-shape only in the first and second quadrants (no negative y-values).
• $f(x)=\frac{1}{x}$ is a hyperbola with two separate curves, not a straight line.
• $f(x)=\sqrt{x}$ only exists for $x\geq0$, with non-negative y-values.
• $f(x)=x$ is a straight line with slope 1, passing through the origin, and includes all positive/negative x and corresponding y values, matching the graph.

Answer:

A. $f(x) = x$