The function f(x) is shown on the graph. ာ 2 3 2 f(x) 1 0 -1 -2 1 -3 -4 -5 2 3 4t Which type of function describes f(x)? Exponential O Logarithmic O Polynomial ○ Rational
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- (a) Draw the exponential function: y = 3x Also identify the asymptote to this function in your figure. (b) Apply translations to the graph of part (a) to draw the function f(x) 3x - 2. = Include the horizontal asymptote of f(x) in your figure. (c) State the domain and the range of f(x). Give the answer in the interval notation.Find the horizontal and vertical asymptotes of the graph of the function using algebraic techniques. You can use a graphing calculator to verify your answer, but not instead of algebra. Briefly describe in words why the functions have the asymptotes. f(x)= ln(x)Runway Length There is a relation between an airplane's weight x and the runway length L required for takeoff. For some airplanes the minimum runway length L in thousands of feet is given by L(x) - 3 log x, where x is measured in thousands of pounds (a) Evaluate L(lOO) and interpret the result. (b) If the weight of an airplane increases tenfold from 10,000 to 100,000 pounds, does the length of the required runway also increase by a factor of 1 O? Explain.
- 2. (6 points) Let f (x) = log2(x + 1). Fill out the table and graph the function. State the domain, range and asymptote. X y -1/2 0 1 3 Domain: (Write an interval) Range: (Write an interval) Asymptote: (Write an equation) -2suppose to make a table so I can graph the functions so can you please make a table for the 2 functions on paper neatly6) Sketch a graph of g(x) = -ln(-x+ 2) over a reasonable domain. You may use technology to assist with this problem, but make sure yo know how to graph it without help going forward. Messages
