Topic
Q:
13. For each set of functions, transform the graph of
\( f(x) \) to sketch \( g(x) \) and \( h(x) \), and state the domain
and range of each function.
a) \( f(x)=x^{2}, g(x)=\left(\frac{1}{2} x\right)^{2}, h(x)=-(2 x)^{2} \)
b) \( f(x)=|x|, g(x)=|-4 x|, h(x)=\left|\frac{1}{4} x\right| \)
Q:
13. For each set of functions, transform the graph of
\( f(x) \) to sketch \( g(x) \) and \( h(x) \), and state the domain
and range of each function.
a) \( f(x)=x^{2}, g(x)=\left(\frac{1}{2} x\right)^{2}, h(x)=-(2 x)^{2} \)
Q:
Find the standard form of the equation of the hyperbola satisfying the given conditions.
Center: \( (0,0) \); focus: \( (0,-6) \); vertex: \( (0,4) \)
Q:
Find the standard form of the equation of the hyperbola satisfying the given conditions.
Center: \( (0,0) \); focus: \( (0,-6) \); vertex: \( (0,4) \)
Q:
Find the standard form of the equation of the hyperbola satisfying the given conditions.
Center: \( (0,0) \); focus: \( (0,-6) \); vertex: \( (0,4) \)
Q:
13. A farmer has 450 m of fencing to enclose a rectangular area and divide it into
ri two sections as shown.
a) Write an equation to express the total area enclosed as a function of the
width. \( 2 x+2 y=450 \)
b) Determine the domain and range of this area function.
c) Determine the dimensions that give the maximum area.
Q:
The percent of women in a country's civilian labor force can be modeled fairly well by the function
\( f(x)=\frac{68.24}{1+1.085 e^{-x / 24.77}} \), where x represents the number of years since 1950. Answer parts a and \( b \).
(a) In 2012 , what percent, to the nearest whole number, of the labor force was comprised of women?
\( \square \% \)
(Do not round until the final answer. Then round to the nearest integer as needed.)
Q:
A research student is working with a culture of bacteria that doubles in size every 90 minutes. The initial
population count was 1225 bacteria. Rounding to five decimal places, write an exponential function,
\( P(t)=P_{0} e^{k t} \), representing this situation. To the nearest whole number, what is the population size
after 5 hours?
Q:
In a mountain range of California, the percent of moisture that falls as snow rather than rain can be approximated by
the function p(hi) \( =76 \ln (h)-597 \), where \( h \) is the altitude in feet and p(h) is the percent of an annual snow fall at the
altitude \( h \). Use the function to approximate the amount of snow at the altitudes 5000 feet and 9000 feet.
The percent of annual precipitation that falls as snow at 5000 feet is approximately \( \square \% \).
(Round to the nearest integer.)
Q:
5. A research student is working with a culture of bacteria that doubles in size every 90 minutes. The initial
population count was 1225 bacteria. Rounding to five decimal places, write an exponential function,
\( P(t)=P_{0} e^{k t} \), representing this situation. To the nearest whole number, what is the population size
after 5 hours?
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