In this problem, we walk through a general procedure of finding horizontal and vertical asymptotes of a function. Fill in the blanks and make the appropriate selections to fill in the details of the following sketch. Let f(x) = -4z²-15z+4 (x+4)(x-4) horizontal line with equation Let's first find all horizontal asymptotes. First, we compute that lim f(x) = Number 1-X is a horizontal asymptote. Next, we evaluate lim f(x), and find that: H-18 lim f(z) exists and is not equal to _lim f(x). Thus, we have found a second horizontal asymptote. I→→∞ I→∞0 lim f(z) exists and is equal to lim f(z). Thus, there isn't a second horizontal asymptote. I→→∞ I→∞0 lim f(x) does not exist. Thus, there isn't a second horizontal asymptote. H→ ∞ Now, we try to find the vertical asymptotes, which can only occur where f(z) is discontinuous. Notice that the function has two discontinuities, at x = -4 and at z = 4. Analyzing f(z) around=-4, we find that At least one of lim f(x), 2-4 lim f(z) is infinite. Thus, z=-4 is indeed a vertical asymptote. z+-4+ Neither lim f(z) nor lim f(z) is infinite. Thus, z = -4 is not a vertical asymptote. z+-4+ I-4 Finally, we analyze f(z) around z = 4. We find that At least one of lim_ f(x), lim f(x) is infinite. Thus, z = 4 is indeed a vertical asymptote. 2+4+ I-4 This tells us that the Neither lim f(z) nor lim f(z) is infinite. Thus, z = 4 is not a vertical asymptote. I-4 2+4+

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10. Given f(x) = Domain of f(x):_ Range of f(x): List all asymptotes of each type. If it does not exist, write None. Horizontal: 3 x x²-x-2 List x-intercept(s). List y-intercept(s). CHART Vertical: Graph the function. Label all asymptotes and intercepts. Set up a chart with domain and range values for points plotted. 6

For the function graphed above, determine each