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Answer1. Give the domain and range in interval notation?2. Write ALL increasing intervals in set notation.3. Write ALL decreasing intervals in set notation.4. What is the maximum/minimum values of graph?5. What is/are the zero(s) of the graph?6. What is the y-intercept?

User Sheikhjabootie
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Answer

1) The domain of this function is (-∞ < x < ∞)

The range of this function is (y ≥ 1).

2) The increasing intervals for this function in set notation is [x ∈ R: x > 3]

3) The decreasing intervals for this function in set notation is [x ∈ R: x < 3]

4) The minimum value of the function is at y = 1.

The graph has no maximum function as it increases till infinity.

5) This grapgh has no zeros because this graph doesn't cross the x-axis.

6) The y-intercept of the graph is at y = 7 or (0, 7).

Step-by-step explanation

We need all of the reuired information just from the graph given.

But before then, we need to note that the graph is for a function that takes the values of an independent variable (x) and obtains a dependent variable (y).

Taking the questions one at a time.

1. Give the domain and range in interval notation?

The domain is the interval of variables that the independent variable of a function (x) can take on.

From the graph, we can see that the graph covers x-coordinate values between negative and positive infinity. So, in interval form,

the domain of this function is (-∞ < x < ∞)

The range is the interval of variables that the dependent variable of a function (y) can take on.

From the graph, we can see that the grapgh covers y-coordinate values between 1 and infinity (it touches 1). In interval form.

the range of this function is (y ≥ 1).

2. Write ALL increasing intervals in set notation.

The increasing intervals refer to the regions of the independent variable (x) where the function increases, that is, regions of x where y increases.

From the graph, we can see that from the point at x=3 upwards, the graph slopes positively, indicating a marked increase.

The increasing intervals for this function in set notation is [x ∈ R: x > 3]

3. Write ALL decreasing intervals in set notation.

The decreasing intervals refer to the regions of the independent variable (x) where the function decreases, that is, regions of x where y decreases.

From the graph, we can see that from the point at x=3 downwards, the graph slopes negatively, indicating a marked decrease.

The decreasing intervals for this function in set notation is [x ∈ R: x < 3]

4. What is the maximum/minimum values of graph?

The maximum/minum values of the graph indicates the points where the function reaches a maximum or a minimum.

From the graph, the minimum value of the function is at y = 1.

The graph has no maximum function as it increases till infinity.

5. What is/are the zero(s) of the graph?

The zero(s) of the graph refers to the point(s) where the graph crosses the x-axis. Since this graph doesn't cross the x-axis, we can conclude that this grapgh has no zeros.

6. What is the y-intercept?

The y-intercept refers to the point where the graph crosses the y-axis.

From the graph, we can see that the graph crosses the y-axis at y = 7.

Hence, the y-intercept of the graph is at y = 7 or (0, 7).

Hope this Helps!!!

User Keerigan
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