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)

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.

$(- \infty, - 2)$

$open paren negative 2 comma 1 close paren$

$(- 2, - \infty)$

$open paren 1 comma negative infinity close paren$

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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