Question

graph the given function. $y=2^{x}$ choose the correct graph on the right. ○a. ○b. ○c. ○d.

Explanation:

Step1: Identify function type

The function $y=2^x$ is an exponential growth function, where the base $2>1$.

Step2: Find key points

Calculate values for small integers:

• When $x=0$, $y=2^0=1$
• When $x=1$, $y=2^1=2$
• When $x=-1$, $y=2^{-1}=\frac{1}{2}$

As $x\to-\infty$, $y\to0$ (horizontal asymptote at $y=0$), and as $x\to+\infty$, $y$ increases rapidly.

Step3: Match to options

Option B shows a curve that passes through $(0,1)$, increases as $x$ increases, approaches $y=0$ as $x$ decreases, which matches the behavior of $y=2^x$. Option A is a decreasing exponential, Option C is linear, Option D is a parabola.

Answer:

B. <The graph that is an increasing exponential curve passing through (0,1), approaching the x-axis as x goes to negative infinity>