Question

which is the graph of $f(x) = \frac{3\sqrt{x}}{4}$?

Explanation:

Step1: Identify domain of the function

The function $f(x)=\frac{3\sqrt{x}}{4}$ has a domain of $x\geq0$, so the graph only exists for non-negative $x$-values. This eliminates the bottom and top-right graphs (they have negative $x$-values plotted).

Step2: Test a point in the function

Choose $x=4$:
$$f(4)=\frac{3\sqrt{4}}{4}=\frac{3\times2}{4}=\frac{6}{4}=0.5$$
So the graph passes through $(4, 0.5)$.

Step3: Match point to graphs

The top-left graph passes through $(4, 0.5)$, while the top-right graph passes through $(4, -0.5)$ (which does not match the positive output of our function for $x=4$).

Answer:

The top-left graph (the one passing through the point (4, 0.5))