138k views
5 votes
Sketch the graph of each function.

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

Sketch the graph of each function. 1) y= 2 (9 X 20 18 to 12 te -6 -2 2 4 6 x-example-1
User Koenmetsu
by
8.8k points

2 Answers

14 votes

Answer:

can yhu see the answer i put?

Explanation:

User Neuront
by
7.7k points
7 votes

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:

| *

| *

| *

| *

| *

| *

| *

| *

| *

| *

| *

| *

--+-------------------

User Sean Curtis
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories