C]. b) What are the vertical asymptotes of at)? Consider the rational function, y = f(a:), shown in the graph given above. a) Find f(1) b". 1", not "x = 1". =3, X Note: If there is more than one, list each separated by a comma: "x Do not include spaces around the equals sign. Type, for example, "x Answer: C] c) If you were to continue the graph to the right, the graph would tend to look like a horizontal line. What is an equation for the horizontal asymptote? Answer: C] 1 Evaluate the given limits using the graph of the function f(a:) = shown above. (w + 5)2 Enter INF for 00, -INF for oo, or DNE if the limit does not exist, but is neither 00 nor 00. If you are having a hard time seeing the picture clearly, click on the picture. It will expand to a larger picture on its own page so that you can inspect it more clearly. A function is said to have a vertical asymptote wherever the limit on the left or right (or both) is either positive or negative infinity. For rational functions (that is functions that are fractions of polynomials) this occurs whenever the numerator is nonzero and the denominator is 0. 3(a: -l 1) For exam le, the function a: = p f( ) 11:2 + 4:7: l 4 has a vertical asymptote at x = 2 since at a: = 2 the denominator is 0. Find each of the following limits. hma:g5:lL=mmmmm 2472- :32 49: + 4 . -3($ + 1) . . 21,113+ m C] help (llmltS) Evaluate the given limits using the graph of the function f(a:) = shown above. e$+1 Enter INF for 00, -INF for oo, or DNE if the limit does not exist, but is neither 00 nor 00. If you are having a hard time seeing the picture clearly, click on the picture. It will expand to a larger picture on its own page so that you can inspect it more clearly. For the function f graphed below, find the following limits. -18 16 1. lim f(x) = help (limits) 2--6 2. lim f(x) = x- - 6+ 3. lim f(x) = 4. lim f(a) = 5. lim f(x) = 2- - 2 6. lim f(a) = x- - 2+ 7. lim f(2) = 8. lim f(x) = 9. lim f(x) = 10. lim f(x) = 11. lim f(x) = 12. lim f(x) = 2-- 00