Pre Calculus Questions & Answers

12. Suppose the function \( f(t) \) is periodic with a period of 4 . Which of the following is not equal to 0 ? a) \( f(7)-4 \) b) \( f(7)-f(3) \) c) \( f(7)-f(15) \) d) \( \frac{f(7)-f(3)}{4} \)

A rectangle is inscribed in a circle of radius \( 2 \) . See the figure. Let \( P = ( x , y ) \) be the point in quadrant I that is a vertex of the rectangle and is on the circle. (a) Express the area \( A \) of the rectangle as a function of \( x \) . (b) Express the perimeter \( p \) of the rectangle as a function of \( x \) . (c) Graph \( A = A ( x ) \) . For what value of \( x \) is \( A \) largest? (d) Graph \( p = p ( x ) \) . For what value of \( x \) is \( p \) largest? 

Begin by graphing \( f(x)=3^{\wedge} \). Then use transformations of this graph to graph the given function: Be sure to graph and give the equation of the asymptote. Use the graph to determine the function's'domain and range. If applicable, use graphing utility to contirm your hand-drawn graphs. \[ g(x)=3^{x}-1 \] Graph \( g(x)=3^{x}-1 \) and its asymptote. Use the graphing tool to graph the function as a solid curve and the asymptote as a dashed line. Click to enlarge graph

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. 7) \( f(x)=-x^{2}(x+1)(x+3) \)

Числа х і у додатні, причому х+у =5. Яке найменше значення може приймати вираз \( \frac{1}{x}+\frac{1}{y} \) ?

Hence, determine a general formula for the pattern \( 0 ;-6 ;-20 ;-42 \ldots \) Simplify your answer as far as possible. ESTION 4 c) \( =-2 x^{2}+2 \) and \( g(x)=2^{x}+1 \) are the defining equations of graphs \( f \) and \( g \) respectively. Write down an equation for the asymptote of \( g \). Sketch the graphs of \( f \) and \( g \) on the same set of axes, clearly showing ALL intercepts with the axes, turning points and asymptotes. Write down the range of \( f \). Determine the maximum value of \( h \) if \( h(x)=3 /(x) \). What transformation does the graph of \( y=f(x) \) undergo in order to obtain the

Graph the exponential function. \[ f(x)=\left(\frac{5}{3}\right)^{-x} \] Plot five points on the graph of the function, and also draw the asymptote. Then click on the graph-a-function button.Make a list of 5 points

Find the vertical and horizontal asymptotes for \( g(x)=\frac{\sqrt{x^{2}-4}}{2-x} \)

3.36. В указанном промежутке с заданным шагом задайте функцию таблицей и по данным этой таблицы постройте ее график: \( \begin{array}{ll}\text { 1) } y=\frac{2}{x}, \frac{1}{2} \leqslant x \leqslant 3 \text {, шаг } h=\frac{1}{2} ; & \text { 2) } y=\frac{x+1}{x-5}, 0 \leqslant x \leqslant 4 \text {, шаг } h=\frac{1}{2}\end{array} \)

Find the relevant domain and range for the following function. The function \( P ( t ) = 25000 + 2200 t \) models the population of a city from years 1980-2005, with \( t = 0 \) representing \( 1980 \) . The domain is \( \square \) (Give answer in correct interval notation. Do not place any spaces.). The range is \( \square \) (Give answer in correct interval notation. Do not place any spaces.).