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!!!