Consider the following rational functions:
- (a) Which of these rational functions has a horizontal asymptote?
- (b) Which of these functions has a slant asymptote?
- (c) Which of these functions has no vertical asymptote?
- (d) Which of these functions has a “hole”?
- (e) What are the asymptotes of the function r(x)?
- (f) Graph y = u(x), showing clearly any asymptotes and x- and y-intercepts the function may have.
- (g) Use long division to find a polynomial P that has the same end behavior as t. Graph both P and t on the same screen to verify that they have the same end behavior.
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Chapter 3 Solutions
Precalculus
- Consider the following rational functions: r(x)=x2x22x1 s(x)=x2+4x3+27 t(x)=x+2x39x u(x)=x225x2+x6 w(x)=x+3x3+6x+9x (a) Which of these rational functions has a horizontal asymptote? (b) Which of these functions has a slant asymptote? (c) Which Of these functions has no vertical asymptote? (d) Which Of these functions has a "hole"? (e) What are the asymptotes of the function r(x) ? (f) Graph y =u(x) , showing clearly any asymptote and x- and y intercepts the function may have. (g) Use long division to find a polynomial P that has the same end behavior as t. graph both P and t on the same screen to verify that they have the sane end behavior.arrow_forwardFind the absolute extrema of f(x) = x3 +5x2-8x+2 on the interval [−1, 2].arrow_forwardLet F(x) = x2 - 3 and G(x) = 6 - x. Find (F/G)(4). (F/G)(4) = (Type an integer or a fraction. Simplify your answer.)arrow_forward
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