Help with some questions

[kalyan601]

Hi, can I have some help with these questions I am not sure how to solve.

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3. Given that f(x) = 1/x, x not equal to 0:
. . .(a) sketch the graph of y = f(x) + 3 and state the equations of the asymptotes.
. . .(b) Find the coordinates of the point where y = f(x) + 3 crosses a coordinate axis.

4. The equation 2x^2 - 3x - (k + 1) = 0, where k is constant, has no real roots. Find the set of possible values of k.

6. The curve C has the equation y = f(x), x not equal to 0, and the point P(2, 1) lies on C. Given that f'(x) = 3x^2 - 6 - 8/(x^2),
. . .(a) find f(x).
. . .(b) Find an equation for the tangent to C at the point P, giving your answer in the form y = mx + c, where m and c are integers.

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For number 3, I can draw the graph but I do not now what it means in part a) about equations of asymptotes. I've worked out part B.

I really don't know how to approach question 4
and for question 6, what does it mean buy f'(x)? I'm not really sure on this question either. I think I should be able to do it but the wording is confusing me.

Thank you for your help in advance!

 

[HallsofIvy]

These are pretty standard "pre-Calculus" or beginning "Calculus" questions. Are you taking one of those classes?

Hi, can I have some help with these questions I am not sure how to solve.

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3. Given that f(x) = 1/x, x not equal to 0:
. . .(a) sketch the graph of y = f(x) + 3 and state the equations of the asymptotes.
. . .(b) Find the coordinates of the point where y = f(x) + 3 crosses a coordinate axis.

4. The equation 2x^2 - 3x - (k + 1) = 0, where k is constant, has no real roots. Find the set of possible values of k.

6. The curve C has the equation y = f(x), x not equal to 0, and the point P(2, 1) lies on C. Given that f'(x) = 3x^2 - 6 - 8/(x^2),
. . .(a) find f(x).
. . .(b) Find an equation for the tangent to C at the point P, giving your answer in the form y = mx + c, where m and c are integers.

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For number 3, I can draw the graph but I do not now what it means in part a) about equations of asymptotes. I've worked out part B.

Do you not know what "asymptote" means? the original function, y= 1/x has two "asymptotes": the horizontal asymptote is y= 0 because as x goes to infinity or -infinity, the graph approaches y= 0 and the vertical asymptote is x= 0 because y goes to infinity as x approaches 0 from above and goes to negative infinity as x approaches 0 from below.

I really don't know how to approach question 4

Do you know the "quadratic formula"? The roots of equation \(\displaystyle ax^2+ bx+ d= 0\) has roots \(\displaystyle x= \frac{-b\pm\sqrt{b^2- 4ac}}{2a}\) Such an equation has "no real roots" if and only if the "discriminant", \(\displaystyle b^2- 4ac\), is negative. What values of k make that negative?

and for question 6, what does it mean buy f'(x)? I'm not really sure on this question either. I think I should be able to do it but the wording is confusing me.

You don't say what course this is but f'(x) is standard notation for the derivative of function f. To find f, you need to take the anti-derivative of f'. Do you know what that is?

Thank you for your help in advance!

 

[kalyan601]

You don't say what course this is but f'(x) is standard notation for the derivative of function f. To find f, you need to take the anti-derivative of f'. Do you know what that is?

Thank for your help, and no I do not know what the anti derivative of f' is
Yeah I am starting the equivalent of Pre Calculus in the UK. (A Level Mathematics) in September and they gave us this homework over the summer to finish.

 

[HallsofIvy]

Well, do you know how to find the derivative? If You do not know what a derivative is I don't see how you can work with f', unless some special definition is given to f' here. Do you know that the derivative of f(x)= xⁿ is f'(x)= nx^{n- 1}? If so then it should not be too much work to go backwards from f'(x)= 3x² - 6x⁰ - 8x^-2,

 

[kalyan601]

Well, do you know how to find the derivative? If You do not know what a derivative is I don't see how you can work with f', unless some special definition is given to f' here. Do you know that the derivative of f(x)= xⁿ is f'(x)= nx^{n- 1}? If so then it should not be too much work to go backwards from f'(x)= 3x² - 6x⁰ - 8x^-2,

Thanks, I've realised that f'(x) means that it has been differentiated once so I needed to integrate it to find f(x)

Thanks for the help!

 

[lookagain]

Do you know the "quadratic formula"? The roots of equation \(\displaystyle ax^2+ bx+ d= 0 \ \ \ \ \) This is a typo.\(\displaystyle \ \ \) It should be \(\displaystyle \ ax^2 + bx + c = 0 \)

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[Quaid]

I am starting the equivalent of Pre Calculus in the UK in September and they gave us this homework over the summer to finish.

Integration skills are a prerequisite for your Pre Calculus course? Yikes.