Working With A Graph

[nycmathguy]

See attachment.

Part (a)

Domain = All real numbers

Range = All real numbers

Part (b)

Zero of f at the point (3, 0). Thus, x = 0 is the only zero of the function.

Part (c)

Increasing: (-4, 1) to (0, 9)

Decreasing: (0, 9) to (3, 0)

Increasing: (3, infinity)

How do we use the graph to do parts (c) and (d)?

 

[MathLover1]

Part (a)

Domain => take a look on x-axis an you see that the courve starts at x=-4 and goes very close to x=5 (there you see a hole)

so, domain is [-4,5)

Range => [0,9]

Part (b)
correction:
Zero of f at the point (3, 0).=>correct

Thus, x = 0 is the only zero of the function.=>incorrect,
the point (3, 0) tells you that x=3 and y=0

recall definition of zero: the value of x for what y=0 (or f(x)=0)


Part (c)

Increasing: (-4, 1) to (0, 9)
correction: no need to name points, all you need is say that increasing [-4,0]

Decreasing: (0, 9) to (3, 0)
all you need is say that increasing [0,3]

Increasing: (3, infinity)=>incorrect
Increasing: [3, 5)

(d)

minimum is at point (3,0)
maximum is at point (0,9)

(e)
The graph of an even function is symmetric about the y- axis.
The graph of an odd function is symmetric about the origin.

in your case the graph is not symmetric about the y- axis nor is symmetric about the x- axis

so, f is neither

 

[nycmathguy]

Part (a)

Domain => take a look on x-axis an you see that the courve starts at x=-4 and goes very close to x=5 (there you see a hole)

so, domain is [-4,5)

Range => [0,9]

Part (b)
correction:
Zero of f at the point (3, 0).=>correct

Thus, x = 0 is the only zero of the function.=>incorrect,
the point (3, 0) tells you that x=3 and y=0

recall definition of zero: the value of x for what y=0 (or f(x)=0)


Part (c)

Increasing: (-4, 1) to (0, 9)
correction: no need to name points, all you need is say that increasing [-4,0]

Decreasing: (0, 9) to (3, 0)
all you need is say that increasing [0,3]

Increasing: (3, infinity)=>incorrect
Increasing: [3, 5)

(d)

minimum is at point (3,0)
maximum is at point (0,9)

(e)
The graph of an even function is symmetric about the y- axis.
The graph of an odd function is symmetric about the origin.

in your case the graph is not symmetric about the y- axis nor is symmetric about the x- axis

so, f is neither

Wonderful, detailed reply.
This is precisely what I am seeking.

1. Is my effort incorrect?

2. If incorrect, why?

3. I will not post daily questions. I often forget that you have a life outside of mathematics.

4. I will post less questions but would like to see a more detailed reply to each thread.

 

[MathLover1]

your solution and my corrections:
Part (a)

Domain = All real numbers=> incorrect

Range = All real numbers=> incorrect


Part (b)

Zero of f at the point (3, 0). => correct
Thus, x = 0 is the only zero of the function.=> incorrect


Part (c)

Increasing: (-4, 1) to (0, 9)=>correction: no need to name points, all you need is say that increasing [-4,0]

Decreasing: (0, 9) to (3, 0)=>correction: all you need is say that increasing [0,3] (we are lookine for x values)

Increasing: (3, infinity)=>incorrect
correction:Increasing: [3, 5)

 

[nycmathguy]

your solution and my corrections:
Part (a)

Domain = All real numbers=> incorrect

Range = All real numbers=> incorrect


Part (b)

Zero of f at the point (3, 0). => correct
Thus, x = 0 is the only zero of the function.=> incorrect


Part (c)

Increasing: (-4, 1) to (0, 9)=>correction: no need to name points, all you need is say that increasing [-4,0]

Decreasing: (0, 9) to (3, 0)=>correction: all you need is say that increasing [0,3] (we are lookine for x values)

Increasing: (3, infinity)=>incorrect
correction:Increasing: [3, 5)

Ok.