Math  /  Calculus

QuestionConsider the function in the graph to the right. The function has a relative maximum of \qquad at x=x= \square The function has a relative minimum of \square at x=x= \square The function is increasing on the interval(s): \square The function is decreasing on the interval(s): \square The domain of the function is: \square
The range of the function is: \square For increasing and decreasing, separate multiple intervals with commas.

Studdy Solution

STEP 1

1. The function is continuous and differentiable over the given domain.
2. The graph provides accurate information about the function's behavior.
3. The relative maximum and minimum are clearly marked on the graph.

STEP 2

1. Identify the relative maximum and minimum points.
2. Determine the intervals where the function is increasing and decreasing.
3. Define the domain and range of the function.

STEP 3

Identify the relative maximum point on the graph. According to the image description, the relative maximum occurs at approximately (0,7) (0, 7) .

STEP 4

Identify the relative minimum point on the graph. According to the image description, the relative minimum occurs at approximately (7,3) (-7, -3) .

STEP 5

Determine the intervals where the function is increasing. The function increases from the relative minimum to the relative maximum, which is from x=7 x = -7 to x=0 x = 0 .

STEP 6

Determine the intervals where the function is decreasing. The function decreases before reaching the relative minimum and after the relative maximum. This occurs from x=10 x = -10 to x=7 x = -7 and from x=0 x = 0 to x=10 x = 10 .

STEP 7

Define the domain of the function. Based on the x-axis range in the image description, the domain is [10,10] [-10, 10] .

STEP 8

Define the range of the function. Based on the y-axis range and the relative maximum and minimum points, the range is [3,7] [-3, 7] .
The function has a relative maximum of 7 7 at x=0 x = 0 .
The function has a relative minimum of 3 -3 at x=7 x = -7 .
The function is increasing on the interval(s): (7,0) (-7, 0) .
The function is decreasing on the interval(s): (10,7),(0,10) (-10, -7), (0, 10) .
The domain of the function is: [10,10] [-10, 10] .
The range of the function is: [3,7] [-3, 7] .

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