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Use the graph of the function to estimate the intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.) increasing decreasing y 6 5 4 3 2 4 X -6 -5 -4 -3 -2 -1 2 3 4 5 6 |-1| ) + 5 6

Use the graph of the function to estimate the intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.) increasing decreasing y 6 5 4 3 2 4 X -6 -5 -4 -3 -2 -1 2 3 4 5 6 |-1| ) + 5 6

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter7: Exponents And Exponential Functions
Section7.6: Transformations Of Exponential Functions
Problem 63PPS
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please explain how to solve this equation.

### Understanding the Behavior of Functions #### How to Identify Increasing and Decreasing Intervals This section will guide you through estimating the intervals on which a given function is increasing or decreasing using its graph. #### Example Exercise: Use the graph of the function to estimate the intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.) **Increasing:** **Decreasing:** #### Explanation of the Graph: The graph displayed is a continuous curve on a Cartesian plane with the x-axis ranging from -6 to 6 and the y-axis ranging from -6 to 6. The curve shows the following behavior: 1. The function decreases from \( x = -6 \) up to approximately \( x = -1 \). 2. The function starts increasing from approximately \( x = -1 \) up to approximately \( x = 2 \). 3. The function decreases again from approximately \( x = 2 \) up to approximately \( x = 4 \). 4. The function increases from approximately \( x = 4 \) up to approximately \( x = 5 \). 5. The function decreases from approximately \( x = 5 \) onwards. ### Identifying Intervals: - **Increasing Intervals:** The function is rising upwards on these sections. - From approximately \( x = -1 \) to \( x = 2 \) - From approximately \( x = 4 \) to \( x = 5 \) - **Decreasing Intervals:** The function is falling downwards on these sections. - From \( x = -6 \) to approximately \( x = -1 \) - From approximately \( x = 2 \) to approximately \( x = 4 \) - From approximately \( x = 5 \) onwards You can use this information to accurately determine and write the intervals in interval notation for where a function is increasing or decreasing.
Transcribed Image Text:### Understanding the Behavior of Functions #### How to Identify Increasing and Decreasing Intervals This section will guide you through estimating the intervals on which a given function is increasing or decreasing using its graph. #### Example Exercise: Use the graph of the function to estimate the intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.) **Increasing:** **Decreasing:** #### Explanation of the Graph: The graph displayed is a continuous curve on a Cartesian plane with the x-axis ranging from -6 to 6 and the y-axis ranging from -6 to 6. The curve shows the following behavior: 1. The function decreases from \( x = -6 \) up to approximately \( x = -1 \). 2. The function starts increasing from approximately \( x = -1 \) up to approximately \( x = 2 \). 3. The function decreases again from approximately \( x = 2 \) up to approximately \( x = 4 \). 4. The function increases from approximately \( x = 4 \) up to approximately \( x = 5 \). 5. The function decreases from approximately \( x = 5 \) onwards. ### Identifying Intervals: - **Increasing Intervals:** The function is rising upwards on these sections. - From approximately \( x = -1 \) to \( x = 2 \) - From approximately \( x = 4 \) to \( x = 5 \) - **Decreasing Intervals:** The function is falling downwards on these sections. - From \( x = -6 \) to approximately \( x = -1 \) - From approximately \( x = 2 \) to approximately \( x = 4 \) - From approximately \( x = 5 \) onwards You can use this information to accurately determine and write the intervals in interval notation for where a function is increasing or decreasing.
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