Graph of A Given Function

[nycmathguy]

Section 1.5
Question 94

See attachment.

Part (a)

Domain = All real numbers.

Range = [-4, 9]

Part (b)

The only zero of this function that I can see on the graph is x = 3.

Part (c)

Increasing open interval: (-4, 9) & (3, infinity)

Constant: (0, 3)

I don't see a decreasing interval. Can a constant interval also be a decreasing or Increasing open interval?

Part (d)

I'm not sure about the relative minimum and relative maximum. The definition as stated in the textbook is not clear to me.

Part (e)

I say the function is symmetric about the y-axis and thus it is even.

You say?

 

[MathLover1]

Part (a)

Domain = [-4, 5) ( remember domain is all x values used)

Range = [0, 9] ( remember range is all y values used)

Part (b)

your answer is correct

Part (c)

Increasing open interval:
you see that from the point (-4,1) to the point (0,9) graph is increasing
also from the point (-4,1) to the point (0,9) to (5,9) graph is increasing
interval: (-4,0) & (3, 5)


Constant: (3, 3.5) (flat line is from x=3 to x=3.5 approximately)

decreasing interval:
observe the graph from x=0 to x=3, the graph is decreasing from point (0,9) to point (3,0)

so, decreasing interval is: (0,3)


Part (d)

the relative minimum is the lowest point on a graph and in this case it is (3,0)
and relative maximum is the highest point on a graph and in this case it is (0,9)


Part (e)

neither even nor odd

If a function is even, the graph is symmetrical about the y-axis. => your graph is not symmetrical about the y-axis

If the function is odd, the graph is symmetrical about the origin. => your graph is not symmetrical about the origin

 

[nycmathguy]

Part (a)

Domain = [-4, 5) ( remember domain is all x values used)

Range = [0, 9] ( remember range is all y values used)

Part (b)

your answer is correct

Part (c)

Increasing open interval:
you see that from the point (-4,1) to the point (0,9) graph is increasing
also from the point (-4,1) to the point (0,9) to (5,9) graph is increasing
interval: (-4,0) & (3, 5)


Constant: (3, 3.5) (flat line is from x=3 to x=3.5 approximately)

decreasing interval:
observe the graph from x=0 to x=3, the graph is decreasing from point (0,9) to point (3,0)

so, decreasing interval is: (0,3)


Part (d)

the relative minimum is the lowest point on a graph and in this case it is (3,0)
and relative maximum is the highest point on a graph and in this case it is (0,9)


Part (e)

neither even nor odd

If a function is even, the graph is symmetrical about the y-axis. => your graph is not symmetrical about the y-axis

If the function is odd, the graph is symmetrical about the origin. => your graph is not symmetrical about the origin

You said:

Part (c)

Increasing open interval:
you see that from the point (-4,1) to the point (0,9) graph is increasing.

This part of your reply is clear.

You said:

also from the point (-4,1) to the point (0,9) to (5,9) graph is increasing.

Where is the point (5, 9) on the graph?

I don't see the interval: (-4,0) & (3, 5). Where is the point (3, 5)? Where is the point (-4, 0)?

You said:

Constant: (3, 3.5) (flat line is from x=3 to x=3.5 approximately).

I thought a constant is a straight line in any direction on the xy-plane. I don't understand your constant reply. Please, explain.

You said:

decreasing interval:
observe the graph from x=0 to x=3, the graph is decreasing from point (0,9) to point (3,0).

You mean x = 0 at the origin to x = 3, where the graph of the function touches the x-axis aka
the y = 0 line. Yes?

You said:

so, decreasing interval is: (0,3)

Given the points that you made known, that is,
(0, 9) and (3, 0), the decreasing open interval is the value of the x-coordinate for each point forming our decreasing open interval (0, 3).

Yes?

 

[MathLover1]

c) sorry, my bad, I accidentally put 5 instead of 0: (3, 5) should be (3,0) : interval: (-4,0) & (3, 0)

a constant is NOT a straight line in any direction on the xy-plane, it's a line parallel to x-axis or lie on x-axis
that is not part of the graph from x = 0 at the origin to x = 3, it is

Where is the point (5, 9) on the graph?-> you see that white circle (so called a hole) on the end of the graph
coordinates of the hole are x=5 and y=9

decreasing interval: yes, graph from x=0 to x=3 lie on x-axis

 

[nycmathguy]

c) sorry, my bad, I accidentally put 5 instead of 0: (3, 5) should be (3,0) : interval: (-4,0) & (3, 0)

a constant is NOT a straight line in any direction on the xy-plane, it's a line parallel to x-axis or lie on x-axis
that is not part of the graph from x = 0 at the origin to x = 3, it is

Where is the point (5, 9) on the graph?-> you see that white circle (so called a hole) on the end of the graph
coordinates of the hole are x=5 and y=9

decreasing interval: yes, graph from x=0 to x=3 lie on x-axis

Thanks. I will give you a break during the week by not posting daily threads. I see myself rushing through the textbooks. My anxiety continues to take control over everything I do, especially math. God is a jealous God, according to the Bible. I have replaced Bible study time for math. No wonder I can't get out of the hole.