Understanding Quadratic Functions and Rational Functions with Asymptotes

[girlsridemx2]

i have a few questions that i just can't seem to understand, if you could PLEASE help me i'd appreciate it!
Consider the quadratic function f(x)=2x^2+4x-3
what is the domain and range of f(x)?

and
Find ALL asymptotes of the function f(x)=x^2-x-12
______________
x-2
* that's suppose to be over x-2

and lastly Find the x- and y- intercepts of f(x)= x^2-x-12
____________
x-2

They might be SUPER easy to you guys but I am just not understanding. Thanks for the time that you've looked over this.
email me at girlsridemx2@yahoo.com



and if at all possible write the equation of a rational function that has vertical asymptotes at x=2 and x=3 and a horizontal asymptote at y=-2


yeah so I am really lost

 

[rocomath]

1 - what makes a function discontinuous? is a quadratic equation continuous throughout? think division by 0.

2 - if your numerator contains the highest power, what happens? what if your denominator contains the highest power? 1/x^n = 0

3 - set it equal to 0 then factor.

 

[girlsridemx2]

Thanks! How do i find the intervals off(x)=2x^2+4x-3 increasing intervals and the decreasing f(x) intervals?

one more...
Let f(x)=a(x-h)^2+k be a quadratic function such that a>0 qne k<0. How many x- intercepts does f(x) have? I am totally lost.



If i could find out how to find the x intercept it would be great

Find the x intercepts of the quadratic function f(x)=2(x-3)^2-4


Thank you times 1 million for all the help your a math genius!

 

[girlsridemx2]

so what are the asymptotes of that last problem?

 

[cristo]

Thanks! How do i find the intervals off(x)=2x^2+4x-3 increasing intervals and the decreasing f(x) intervals?

Find the turning points, then classify whether they are maxima or minima.

one more...
Let f(x)=a(x-h)^2+k be a quadratic function such that a>0 qne k<0. How many x- intercepts does f(x) have? I am totally lost.

Well, an x-intercept means the graph crosses the x axis, i.e. it crosses the line y=0. So, if you set the function to zero then you should be able to find the answer.

If i could find out how to find the x intercept it would be great

Find the x intercepts of the quadratic function f(x)=2(x-3)^2-4Thank you times 1 million for all the help your a math genius!

Use a similar method for this question.

As an aside, please note that with homework questions, you must show your work before we can help you, and full solutions to homework type questions should never be given. See the PF guidelines here

 

[bakin]

To find X intercepts, you set the problem equal to 0 and solve.

 

[rocomath]

what does a horizontal tangent tell you? and how can you use that information to find the maxima or minima?

asymptotes: horizontal, how can you use the powers of your exponents to determine the horizontal asymptote; vertical, how do you even get a vertical asymptote?

 

[girlsridemx2]

okay,,,,to find the degree of
g(x)=x(x^2=9)^3(x-1)^2
the leading coefficient is 9 right and the degree i though would be 3 but the girl at the math lab says that i should times the 2 and 3 to get 6 as the degree. Am i right or is the girl at the math lab right?
thanks,

 

[rocomath]

ok now I'm confused as to what the problem is, and what the question is. start over!

equation:

question:

 

[girlsridemx2]

Okay, i have to state the degree abnd the leading coefficient of
g(x)= x(x^2+9)^3(x-1)^2.

I was thinking the leading coefficient was 9
and the degree is 3, but the lady at the math lab yesterday told me i have to times the 2 and the 3 together because its in the same group...so what would the answer be for the degree of that entire problem...3 or 6?

 

[rocomath]

and if at all possible write the equation of a rational function that has vertical asymptotes at x = 2 and x = 3 and a horizontal asymptote at y = -2

how does a vertical asymptote arise? when the denominator is 0 correct? so how can you write 2 and -3 in the denominator in terms of an equation to where it will equal 2 and -3. now for your numerator, what is the simplest way in Calculus to determine the horizontal asymptote? it's simply by the power of the degrees, so how can you set up your equation to where you can get y = -2.

 

[cristo]

Well, you should firstly recall the definitions of the two terms: the degree of the polynomial is the highest power of x that it contains. The leading coefficient is the coefficient of this term.

So, the largest power of x of the polynomial will be obtained by multiplying the largest terms in the brackets together. What is the largest power in (x^2+9)^3? What is the largest power in (x-1)^2?

I don't know why you're throwing in loads of different questions though!

 

[rocomath]

the lady at the math lab yesterday told me i have to times the 2 and the 3 together because its in the same group

so she is saying that you can simply add the exponents bc the bases are the same? i fail to see how the bases are the same for this equation.

g(x)= x(x^2+9)^3(x-1)^2

going back to our exponent rules or whatever it's called:

a^2 x a^3 = a^2+3

(x^2+9)^3 x (x-1)^2 = ?

ok nvm i read your reply wrong. she says you can multiply the power 2 from x^2+9 by it's power 3?

anyways, read what cristo said.