Math / Geometry

Question07 Fill in the Blank Dropdown
The graph of $\mathrm{g}(\mathrm{x})$ is shown on the grid below. Answer the questions that follow. (a) On what interval is the function increasing? $(-\infty,-2) \cup(0,2) \sim$ (b) On what interval is the function decreasing? $(-2,0) \cup(2, \infty)$ (c) On what interval is the function $g(x)>0$ ? $(-3,3)$ (d) On what interval is the function $g(x)<0$ ? $(-3,3)$
Parts (e)-(h) on following slide Search

Studdy Solution

STEP 1

1. The function $g(x)$ is a continuous piecewise function.
2. The graph provides visual information about the intervals where the function increases, decreases, and changes sign.

STEP 2

1. Determine the intervals where the function is increasing.
2. Determine the intervals where the function is decreasing.
3. Determine the intervals where the function is positive.
4. Determine the intervals where the function is negative.

STEP 3

Identify the intervals where the function is increasing by observing the graph. The function increases on the intervals where the slope of the graph is positive.
From the graph description, the function is increasing on the intervals: $(-\infty, -2) \cup (0, 2)$

STEP 4

Identify the intervals where the function is decreasing by observing the graph. The function decreases on the intervals where the slope of the graph is negative.
From the graph description, the function is decreasing on the intervals: $(-2, 0) \cup (2, \infty)$

STEP 5

Identify the intervals where the function is positive by observing the graph. The function is positive where it is above the x-axis.
From the graph description, the function is positive on the interval: $(-3, 3)$

STEP 6

Identify the intervals where the function is negative by observing the graph. The function is negative where it is below the x-axis.
From the graph description, the function is negative outside the interval: $(-3, 3)$
The intervals for each condition are: (a) Increasing: $(- \infty, -2) \cup (0, 2)$ (b) Decreasing: $(-2, 0) \cup (2, \infty)$ (c) Positive: $(-3, 3)$ (d) Negative: Outside $(-3, 3)$

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Studdy Solution

STEP 1

1. The function $g(x)$ is a continuous piecewise function.
2. The graph provides visual information about the intervals where the function increases, decreases, and changes sign.

STEP 2

1. Determine the intervals where the function is increasing.
2. Determine the intervals where the function is decreasing.
3. Determine the intervals where the function is positive.
4. Determine the intervals where the function is negative.

STEP 3

Identify the intervals where the function is increasing by observing the graph. The function increases on the intervals where the slope of the graph is positive.
From the graph description, the function is increasing on the intervals: $(-\infty, -2) \cup (0, 2)$

STEP 4

Identify the intervals where the function is decreasing by observing the graph. The function decreases on the intervals where the slope of the graph is negative.
From the graph description, the function is decreasing on the intervals: $(-2, 0) \cup (2, \infty)$

STEP 5

Identify the intervals where the function is positive by observing the graph. The function is positive where it is above the x-axis.
From the graph description, the function is positive on the interval: $(-3, 3)$

STEP 6

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Studdy Solution

STEP 1

1. The function g(x) g(x) g(x) is a continuous piecewise function.2. The graph provides visual information about the intervals where the function increases, decreases, and changes sign.

STEP 2

1. Determine the intervals where the function is increasing.2. Determine the intervals where the function is decreasing.3. Determine the intervals where the function is positive.4. Determine the intervals where the function is negative.

STEP 3

STEP 4

Identify the intervals where the function is decreasing by observing the graph. The function decreases on the intervals where the slope of the graph is negative.From the graph description, the function is decreasing on the intervals: (−2,0)∪(2,∞) (-2, 0) \cup (2, \infty) (−2,0)∪(2,∞)

STEP 5

Identify the intervals where the function is positive by observing the graph. The function is positive where it is above the x-axis.From the graph description, the function is positive on the interval: (−3,3) (-3, 3) (−3,3)

STEP 6

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. The function $g(x)$ is a continuous piecewise function.
2. The graph provides visual information about the intervals where the function increases, decreases, and changes sign.

1. Determine the intervals where the function is increasing.
2. Determine the intervals where the function is decreasing.
3. Determine the intervals where the function is positive.
4. Determine the intervals where the function is negative.

Identify the intervals where the function is decreasing by observing the graph. The function decreases on the intervals where the slope of the graph is negative.
From the graph description, the function is decreasing on the intervals: $(-2, 0) \cup (2, \infty)$

Identify the intervals where the function is positive by observing the graph. The function is positive where it is above the x-axis.
From the graph description, the function is positive on the interval: $(-3, 3)$