Is my maths good for d1

Original post by Jane122

whats the range of this graph y=2/x if the domain is x>2 ?

@SeanFM @maths123

Consider what y is when x=2 and what happens as x tends to infinity.

Reply 22

Original post by SeanFM

Not completely incorrect :smile:

but not completely correct either.

If you were given a graph and asked to find the range of the function on the graph, how would you find it? What is the definition of the range?

smallest y value and y=0 is the smallest asymptote so?

Reply 23

Original post by NotNotBatman

Consider what y is when x=2 and what happens as x tends to infinity.

i have another q.
idk how to draw 2x+3/x-1 (her,x>1)
and find the domain and range of f-1(X)

I GOT THE RANGE OF F-1(X) AS YER, Y>1 since the domain on f(X) IS THE RANGE OF F-1(X)

Reply 24

Original post by Jane122

smallest y value and y=0 is the smallest asymptote so?

No, the range is not the smallest y value :smile:

it is the range of ....

Spoiler

That should help you answer your question and to see why y>0 is not completely correct but not completely incorrect.

Reply 25

Original post by Jane122

i have another q.
idk how to draw 2x+3/x-1 (her,x>1)
and find the domain and range of f-1(X)

I GOT THE RANGE OF F-1(X) AS YER, Y>1 since the domain on f(X) IS THE RANGE OF F-1(X)

For

\frac{2x+3}{x-1}

divide top and bottom by x, so that you have

\frac{2 +\frac{3}{x}}{1 - \frac{1}{x}}

and observe what happens for large values of x.

Reply 26

Original post by SeanFM

No, the range is not the smallest y value :smile:

it is the range of ....

Spoiler

That should help you answer your question and to see why y>0 is not completely correct but not completely incorrect.

i'm still confused. I don't know what the range is. so it was y>0?

Reply 27

Original post by NotNotBatman

For

\frac{2x+3}{x-1}

divide top and bottom by x, so that you have

\frac{2 +\frac{3}{x}}{1 - \frac{1}{x}}

and observe what happens for large values of x.

why tho?

also i drew the graph of x^3+1 so is the range y> than equal to 1? but theres also negative Y values oh I'm confused gosh

@SeanFM

(edited 7 years ago)

Reply 28

Original post by Jane122

i'm still confused. I don't know what the range is. so it was y>0?

I have told you the definition of the range, so what is the definition? :smile:

(and hence what is the answer to your question?)

Reply 29

Original post by SeanFM

I have told you the definition of the range, so what is the definition? :smile:

(and hence what is the answer to your question?)

the y values that exist? so y>0?

Reply 30

Original post by Jane122

why tho?

also i drew the graph of x^3+1 so is the range y> than equal to 1? but theres also negative Y values oh I'm confused gosh

Why? Because it makes it easier to see what's happens. You could just sub in large values of x into the calculator, but sometimes that's not enough.

The range for

y =x^3 +1

y \in \mathbb{R}

if the domain is unrestricted.

Reply 31

Original post by NotNotBatman

Why? Because it makes it easier to see what's happens. You could just sub in large values of x into the calculator, but sometimes that's not enough.

The range for

y =x^3 +1

y \in \mathbb{R}

if the domain is unrestricted.

oh okay!! but you know how i put the graph passing through 1 do i ignore the 1 then? i don't get restricted and unrestricted..

Reply 32

Original post by Jane122

the y values that exist? so y>0?

Yes, the y values that exist :smile:

now remember y = 2/x where x > 2.

So tell me, if y>0 (every value of y that is greater than 0) exists, when is y = 100? How about 10000?

Reply 33

Original post by SeanFM

Yes, the y values that exist :smile:

now remember y = 2/x where x > 2.

So tell me, if y>0 (every value of y that is greater than 0) exists, when is y = 100? How about 10000?

i said y>0 first....

would it be 0<y<1?

(edited 7 years ago)

Reply 34

Original post by Jane122

i said y>0 first....

would it be 0<y<1?

See, well done :h:

hopefully you understand that now and how to tackle questions in the future (just by asking yourself what y values exist for the given x values)

Reply 35

Original post by SeanFM

See, well done :h:

hopefully you understand that now and how to tackle questions in the future (just by asking yourself what y values exist for the given x values)

thank you!!!!!! :biggrin:

Reply 36

Original post by Jane122

oh okay!! but you know how i put the graph passing through 1 do i ignore the 1 then? i don't get restricted and unrestricted..

What do you mean ignore the 1? The range is not determined by where this graph is crossing the y axis, it is from the smallest y can be and the greatest y can be and that is between

- \infty

and

\infty

An exception is when there is a discontinuous curve, this is where there would be a gap in the curve.

Unrestricted domain means x can be any real number, written as

x \in \mathbb{R}

Restricted domain is where the function can only take on a certain range of x values. So if it was

y = x^3 + 1 , -3 \leq x\leq 3

then the domain is restricted from

x=-3

x=3

Reply 37