16. Use f(t) = 4 tan(t - 7) to answer the questions below.(a) Find the period.(b) Find one horizontal intercept.(c) Find one vertical asymptote.(d) Find the range.

Given that the function ft=4tant-7. Find a) The period b) One horizontal intercept. c) One vertical asymptote. d) The range. The general equation of tangent function is of the form y=AtanπTt-h+k. where A is the amplitude, T is the period, h is the left/ right shift and k is the up/ down shift.a) To find the period of the function, Compare the given equation with the general equation y=AtanπTt-h+k. Here T is the period. On comparing, πT=1π=T Hence, the period is π. b) To find the horizontal intercept, Put ft=0. 4tant-7=0tant-7=0t-7=tan-10 =0t=7 Hence, one of the horizontal intercept is (7,0). c) To find one vertical asymptote, Find the value of the function, when the limit of the function tends to ±∞. The value of tangent function tends to infinity, when t-7=π2. That is t=π2+7 Hence, the vertical asymptote is t=π2+7. d) To find the range of the function, The range of the function is the output value of the given function. Here the output value is set of all real numbers. Hence, the range of the given function is -∞,∞.