Question

which is the graph of $g(x) = (2)^{x}$? (followed by three graphs with coordinate axes and orange curves)

Explanation:

Step1: Identify function type

The function is $f(x)=2^x$, an exponential growth function.

Step2: Test key x-values

• For $x=-2$: $f(-2)=2^{-2}=\frac{1}{4}=0.25$
• For $x=-1$: $f(-1)=2^{-1}=\frac{1}{2}=0.5$
• For $x=0$: $f(0)=2^0=1$
• For $x=1$: $f(1)=2^1=2$
• For $x=2$: $f(2)=2^2=4$

Step3: Match values to graphs

These values correspond to the first graph, which increases as $x$ increases, passing through $(0,1)$ and rising to $(2,4)$.

Answer:

The first graph (left-most graph, increasing from left to right, passing through (0,1) and rising to (2,4))