anonymous
  • anonymous
For y=(1/2)x-sinx where 0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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yuki
  • yuki
To find the domain, all you care about is 1), is the denominator = 0 ? 2), is the number inside a square root negative ?
yuki
  • yuki
in your case, x/2 is a polynomial and sin(x) is a trig function with no vertical asymptotes, so the denominator is never 0 and we don't have to worry about imaginary numbers.
yuki
  • yuki
trig functions oscilate, so there is no need to consider about horizontal asymptotes.

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yuki
  • yuki
for the same reason, slant asymptotes will not be there
dumbcow
  • dumbcow
For domain it is provided, 0infinity, but in this case with a trig function there is no limit because its cyclical. x-intercept, set y=0 sinx = 1/2x
yuki
  • yuki
vertical asymptotes are the points where your function has a denominator equal to zero, but not the numerator. again, since there were not problem with the domain we don't have to worry about that.
yuki
  • yuki
for the x-int, solve for x when y=0 for the y-int, solve for y when x=0.
yuki
  • yuki
to see whether f is increasing or decreasing, you will find the derivative of your function f. if f'>0, then the function is increasing. the opposite would work similarly.
yuki
  • yuki
to see whether f is concave up or down, you will find the second derivative of your function f. if f">0, then it is concave up. the opposite is similar.
yuki
  • yuki
let me know if you need more help.
anonymous
  • anonymous
Wow, thanks a lot!

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