10. If f(c) is undefined but the limit as x approaches c is 7, what does that mean? a. x7 is a vertical asymptote b. (c,7) is a hole c. x - cis a vertical asymptote d. (7,c) is a hole e. none of these

Which of the following functions has exactly one vertical asymptote when graphed? a) f(x) b) f(x): c) f(x) = 6 x²-3x 6x x² – 3x 6x² - 18x X d) B and C

5. For the function f(x) 6x² + 29x - 5 x² + 8x + 15 identify any horizontal or vertical asymptote as well as any removable discontinuity. Use limits to support your answer. =

18.) Explain why a lim √√x-3 X-73 b.) lim x²-4 C.) f(x)= 5-5; if x ²1 22, if x = 1 x-> lim f(x) S 5x², if x ²-1 1 (2x +1, if x = -1³ to the curve Determine the equation of the at the given value of x b.) y=x²-x - where x = -2 • pg. 60, #1. Explain why lim does not exist X-1 X-1 #3. For the function shown below, determine the following 41Y lim G.) f(x) 3 X-71 y=f(x) b) lim f(x) X-72 1-4 Clim fo X-74 O 4 5 19.) X-2 X²-4x+4 I the 2 given limit does not exist do lim X-72 √x-2 elim IXI X-70 X fi foo tangent 3 lim fon X-7-1 of each function d) values of x for which f is discontinuous

5x? 9. Let g(x)=- x² - 49 a. Find the domain b. Identify any asymptotes (vert. and horiz.)

Which of the following statements imply that has a vertical asymptote at ? *Make sure to select the option that lists all possible statements." 1. 11. III. IV. V. VI. a. I, II, III and VI b. Il and VI c. 1, II and VI d. I and II e. f. I and VI 2=3 IV and V lim g(x) = ∞ lim g(x) = ∞ 2-3 lim g(x)=x lim g(z) = 3 lim g(x) = 3 200 lim g(z) = -00 2-37

Graph the following make sure to label all asymptotes, end behavior, x and y intercepts, and holes!

Find all vertical asymptotes of the given function. x - 2 4) f(x) = x3-4x A) x =0, x = -2, x = 2 Find the limit. 5) lim X-00 A) 6 6x³+4x² x - 7x² B) x = 0, x = 2 B) - 17/12 C) x = -2, x = 2 00 D) x = 0, x = -2 D) -

21 3. Using the function, f (x) = 1+6-0.3* a) Find the y-intercept b) Find the horizontal asymptotes c) State the end behavior of the graph using limit notation.