Given the graph of the following function, determine the intervals on which f(x)f\left(x\right)f(x) is decreasing.

( − 2 , 1 ) \left(-2,1\right)

Given the graph of the following function, determine the intervals on which f ( x ) f\left(x\right) f ( x ) is decreasing.

Using the graph of the following function, determine the intervals on which the function is decreasing. Okay. So when solving these types of problems, what we need to do is imagine that we have a little person that is walking from left to right on our graph. As they go uphill, the function would be increasing. As they go downhill, the function would be decreasing. So that's what we need to focus on. Now looking at this graph, if we're going from left to right, there's really only one place that I can see where we're going to be going downhill, and that's right there. Those that we're going to be going uphill here, we're going uphill there, but this person's gonna be going downhill right about there. So that's where the function is going to be decreasing. So if I wanna write where my function is decreasing, that's going to be this situation, which we can see we start here at negative 2, and then we go all the way over here to positive 1 on the x axis. This is going to be the values or the interval on which my function is decreasing, and that's the solution.

Given the graph of the following function, determine the intervals on which f ( x ) f\left(x\right) f ( x ) is decreasing.

( − 2 , 1 ) \left(-2,1\right)

( − ∞ , − 2 ) \left(-\infty,-2\right)

( − 2 , − ∞ ) \left(-2,-\infty\right)

( 1 , − ∞ ) \left(1,-\infty\right)

Given the graph of the following function, determine the interval...

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0. Functions4h 53m
1. Limits and Continuity2h 2m
2. Intro to Derivatives1h 33m
3. Techniques of Differentiation2h 18m
4. Derivatives of Exponential & Logarithmic Functions1h 16m
- Derivatives of Exponential & Logarithmic Functions
  1h 16m
5. Applications of Derivatives2h 19m
6. Graphical Applications of Derivatives6h 0m
7. Antiderivatives & Indefinite Integrals48m
- Antiderivatives
  17m
- Indefinite Integrals
  31m
8. Definite Integrals4h 36m
9. Graphical Applications of Integrals1h 43m
- Area Between Curves
  1h 19m
- Introduction to Volume & Disk Method
  23m
10. Integrals of Inverse, Exponential, & Logarithmic Functions21m
- Integrals of Exponential Functions
  14m
- Integrals Involving Logarithmic Functions
  7m
11. Techniques of Integration2h 7m
- Integration by Parts
  1h 37m
- Improper Integrals
  29m
12. Trigonometric Functions6h 54m
13: Intro to Differential Equations2h 23m
14. Sequences & Series1h 53m
15. Power Series2h 19m
- Power Series & Taylor Series
  2h 19m

0. Functions

Properties of Functions

Business Calculus

0. Functions

Properties of Functions

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Multiple Choice

Given the graph of the following function, determine the intervals on which $f\left(x\right)$ is decreasing.

$(- \infty, - 2)$

$open paren negative 2 comma 1 close paren$

$(- 2, - \infty)$

$open paren 1 comma negative infinity close paren$

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Verified step by step guidance

Step 1: Observe the graph of the function f(x). Identify the regions where the slope of the graph is negative, as this indicates that the function is decreasing.

Step 2: Look for intervals where the graph moves downward as x increases. This happens when the derivative f'(x) is less than zero.

Step 3: From the graph, note that the function decreases from x = -∞ to x = -2 and again from x = -2 to x = 1. These intervals correspond to the downward slopes of the graph.

Step 4: Write the intervals of decrease based on the observed behavior of the graph. The intervals are (-∞, -2) and (-2, 1).

Step 5: Verify the intervals by ensuring that the graph does not increase within these ranges. Confirm that the function transitions from decreasing to increasing at x = -2 and x = 1.

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Given the graph of the following function, determine the intervals on which f(x)f\left(x\right)f(x) is decreasing.

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Given the graph of the following function, determine the intervals on which $f\left(x\right)$ is decreasing.