Pre Calculus Questions & Answers

Q:

An exponential function \( f \) has a 3-unit growth factor of 1.76 . a. What is the 1-unit growth factor for \( f \) ? Preview b. What is the 2-unit growth factor for \( f \) ? Preview c. What is the \( \frac{1}{2} \)-unit growth factor for \( f \) ? \[ 1.095 \] Preview

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The graph shown represents the number of bacteria in a dish after a certain number of minutes. It is a function in the form \( f(x)=a \cdot b^{x} \) How many bacteria are in the dish after 9.2 minutes? (Round your answer to the nearest whole number.)

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Выбери промежуток, на котором функция у \( =21 \mathrm{x}^{2} \) будет постоянно возрастать.

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Find \( c \) if \( a=2.19 \mathrm{mi}, b=3.62 \mathrm{mi} \) and \( \angle C=40.5 \) degrees. Enter \( c \) rounded to 3 decimal places. \[ c=\square \mathrm{mi} \] Assume \( \angle A \) is opposite side \( a, \angle B \) is opposite side \( b \), and \( \angle C \) is opposite side \( c \). Question Help: \( \square \) Video Submit Question

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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) \( \frac{f(7)-f(3)}{4} \)

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Завдання з. Побудуйте криволінійні трапеції, у \( =4-x^{2} \) на \( [-1 ; 2] \) б) у \( y=\cos x \) на \( [-\pi / 2 ; \pi / 2] \)

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122. Постройте график функции \( y=-x^{2}+2 x+8 \) и найдите, ис- пользуя график: а) значение функции при \( x=2,5 ;-0,5 ;-3 ; \) б) значения аргумента, при которых \( y=6 ; 0 ;-2 \); в) нули функции и промежутки знакопостоянства; г) промежутки возрастания и убывания функции, область зна- чений функции.

Q:

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? 

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

Q:

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