Graphs functions does y = f(x)

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mathmarauder

Junior Member
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Oct 25, 2008
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I must be missing something.
Im studying for a math test and it seems
at times that the problem is something like
y = some numbers with an x in there
and sometimes it says
f(x) = some numbers with an x in there
does y = f(x) ?
im trying to study for this test so a sample problem is
sketch the graph of the function
y = 2^x-1 (+8)

yet im not finding how to practice that example
though there seems to be samples for things like
f(x) = whatever
 
mathmarauder said:
I must be missing something.
Im studying for a math test and it seems
at times that the problem is something like
y = some numbers with an x in there
and sometimes it says
f(x) = some numbers with an x in there
does y = f(x) ?
im trying to study for this test so a sample problem is
sketch the graph of the function
y = 2^x-1 (+8)

yet im not finding how to practice that example
though there seems to be samples for things like
f(x) = whatever
Click to expand...

'y' and 'f(x)' are used interchangeably. Actually for your problem - that would be irrelevant.

For your graphing problem - I assume the problem statement refers to:

\(\displaystyle y \, = \, 2^{x-1} \, + \, 8\)

You need to think graphical transformation.

You need to know first how to plot:

\(\displaystyle y \, = \, 2^x\)

then transform that by shifting along the x-axis to produce the plot of:

\(\displaystyle y \, = \, 2^{x-1}\)

then transform that by shifting along the y-axis to produce plot of:

\(\displaystyle y \, - \, 8 \, = \, 2^{x-1}\)

and you are done....
 
that was leading to this.

sketch the graph of the function
f(x) = (x-3)/(x^2+x-2)

so far I have..
f(x) = (x-3)/((x-1)(x+2)

(x-1)(x+2) = 0
x-1 = 0 x+2= 0
x = 1 x= -2

from here I am uncertain what to do next.
Any help would be greatly appreciated
 
mathmarauder said:
that was leading to this.

sketch the graph of the function
f(x) = (x-3)/(x^2+x-2)

so far I have..
f(x) = (x-3)/((x-1)(x+2)

(x-1)(x+2) = 0
x-1 = 0 x+2= 0
x = 1 x= -2

from here I am uncertain what to do next.
Any help would be greatly appreciated
Click to expand...

What are the critical points of the given function f(x)?

Does the graph have any horizontal and/or vertical asymptotes?

Where is the y-intercept (if it exists)?
 
Quite a lot of questions :)
I hope I can answer some.
the critical points? I have no idea
horizontal asymptote is 0 ?
vertical asymptotes 1,-2 ?
y-intercept ... i dont know that either
 
mathmarauder said:
Quite a lot of questions :)
I hope I can answer some.
the critical points? I have no idea

What Is the definition of critical point of function (that will give an idea about how to find those)?

horizontal asymptote is 0 ? <<< correct
vertical asymptotes 1,-2 ?<<< correct
y-intercept ... i dont know that either



What Is the definition of y-intercept of function (that will give an idea about how to find that)?
Click to expand...
 
I looked up the definition
"a critical point of a function of several variables is a point at which
the gradient of the function is either the zero vector 0 or is undefined."

So I am guessing the critical points are undefined?
the definition of y-intercept I believe is where the line
crosses the Y axis.

graphing this is my next issue...which is why i dont know where
the Y intercept is.
 
f(x) = (x-3)/(x^2+x-2)

graphing this is my next issue...which is why i dont know where
the Y intercept is.
Click to expand...

You've correctly identified your asymptotes, so you can use a straightforward approach for graphing: just plug in several values of x in each region defined by your vertical asymptotes to see the trend in each region. For example, in the middle region, between 1 and -2, if you plug in 0 for x, you'll get your y intercept (3/2). Calculate about three points in each region, choosing x values near your asymptotes.
 
mathmarauder said:
I looked up the definition
"a critical point of a function of several variables is a point at which
the gradient of the function is either the zero vector 0 or is undefined."

So I am guessing the critical points are undefined?
the definition of y-intercept I believe is where the line
crosses the Y axis.

When it crosses the Y-axis - what is the value of 'x'?

Knowing that - calculate the value of the function (f(x)) - or evaluate - at that 'x'.

The above value of 'y' - is your y-intercept.

Another set of point/s you need to find is where y = 0 - or the x-intercept/s.

Mathm

Are you trying to these problems as a class work? Or are you picking these problems without much guidance?

Graphing this function is quite complicated - you need to know some calculus to catch all the salient points of the graph.

graphing this is my next issue...which is why i dont know where
the Y intercept is.
Click to expand...
 
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