Question

Sketch the graph of each function.

1) y= 2
(9
X
20
18
to
12
te
-6
-2
2
4
6
x

Answer 1

can yhu see the answer i put?

Explanation:

Answer 2

The graph is a decreasing exponential function with an asymptote at
`\(y = 0\)`. The points (0, 2) and (1, 1) are plotted, showcasing the exponential decay behavior.

1. Identify Key Points:

- When
`\(x = 0\), \(y = 2 \cdot \left((1)/(2)\right)^0 = 2\)`.

- As
`\(x\)` increases,
`\(y\)` decreases because the base
`\((1)/(2)\)` is less than 1.

2. Plot Points:

- Plot the point (0, 2).

- As
`\(x\)` increases by 1,
`\(y\)` will be halved. For example, when
`\(x = 1\), \(y = 2 \cdot \left((1)/(2)\right)^1 = 1\). Plot (1, 1).`

- As
`\(x\)` increases further,
`\(y\)` continues to halve.

3. Asymptote:

- As
`\(x\)` approaches negative infinity, the term
`\(\left((1)/(2)\right)^x\)` approaches 0. Therefore, there is a horizontal asymptote at
`\(y = 0\)`.

4. Sketch the Graph:

- Connect the points smoothly, noting the exponential decay trend.

- The graph will approach but never touch the x-axis due to the asymptote.

Below is an updated textual representation of the graph:

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