Question

Directions: Graph each function using a table of Graph each values, then identify its key characteristics.

Answer 1

Answer:

Step-by-step explanation:

Given function is,

$y=(\frac{1}{2})^x$

In the given exponential function,

Base of the function = $\frac{1}{2}$

By the property of an exponential function,

1). If the base is between 0 and 1, function will be a growth function.

2). If the base is greater than 1, function will be a decay function.

Therefore, given function is a decay function.

Input-output table,

x             -2                -1               0                1                 2

y      $(\frac{1}{2})^{-2}=4$     $(\frac{1}{2})^{-1}=2$     $(\frac{1}{2})^{0}=1$   $(\frac{1}{2})^1=\frac{1}{2}$      $(\frac{1}{2})^2=\frac{1}{4}$

By plotting these points we can get the graph of the function.

Domain: (-∞, ∞)

Range: (0, ∞)

y-intercept: 1

Asymptote: y = 0