Tema
Q:
The population of a country in 2021 was approximately 127 million with an annual growth rate of \( 1.06 \% \). At this rate, the
population \( P(t) \) (in millions) can be approximated by \( P(t)=127(1.0106)^{t} \), where \( t \) is the time in years since 2021 .
Part: \( \mathbf{0} / \mathbf{4} \)
Part 1 of 4
(a) Is the graph of \( P \) an increasing or decreasing exponential function?
The graph of \( P \) is (Choose one) \( \mathbf{\nabla} \) exponential function.
Q:
Use the function below to answer the following questions.
\[ n(x)=-e^{x}-1 \]
(a) Use transformations of the graph of \( y=e^{x} \) to graph the given function.
(b) Write the domain and range in interval notation.
(c) Write an equation of the asymptote.
Q:
For the functions \( f(x)=\frac{2}{x+3} \) and \( g(x)=\frac{11}{x+2} \), find the composition \( f \circ g \) and simplify your answer as much as possible. Write
the domain using interval notation.
\( (f \circ g)(x)=\square \)
Q:
Use the function below to answer the following questions.
\[ p(x)=2^{x-1}-1 \]
(a) Use transformations of the graph of \( y=2^{x} \) to graph the given function.
(b) Write the domain and range in interval notation.
(c) Write an equation of the asymptote.
Q:
For the functions \( f(x)=\frac{2}{x+3} \) and \( g(x)=\frac{11}{x+2} \), find the composition \( f \circ g \) and simplify your answer as much as possible. Write
the domain using interval notation.
\( (f \circ g)(x)=\square \)
Q:
Suppose that the functions \( q \) and \( r \) are defined as follows.
\[ \begin{array}{l}q(x)=-x-4 \\ r(x)=-3 x \\ (q \circ r)(1)=\square \\ (r \circ q)(1)=\square\end{array} \]
Find the following.
Q:
Suppose that the functions \( p \) and \( q \) are defined as follows.
\[ \begin{array}{l}p(x)=x+1 \\ q(x)=2 x^{2}+2 \\ \text { Find the following. } \\ \begin{array}{l}(q \circ p)(3)=\square \\ (p \circ q)(3)=\square\end{array}\end{array} \]
Q:
Exercises 11-14: Critical Thinking The formulas for \( f(x) \)
and \( g(x) \) are identical except for their leading coefficients a.
Compare the graphs of \( f \) and \( g \). You may want to support
your answers by graphing \( f \) and \( g \) together.
11. \( f(x)=x^{2}, g(x)=2 x^{2} \)
Q:
d) \( \sqrt{1-\left(\frac{4}{5}\right)^{2}}+\frac{4}{5} \sqrt{\frac{1}{64}}= \)
Q:
Write the equation of the hyperbola \( 4 x^{2}-25 y^{2}+8 x+250 y-721=0 \) in standard form
\[ \frac{(x-h)^{2}}{a^{2}}-\frac{(y-k)^{2}}{b^{2}}=1 \]
Where:
\( \mathrm{h}=\square \)
\( \mathrm{k}=\square \)
\( \mathrm{a}=\square \)
\( \mathrm{b}=\square \)
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