Match each transformation of function \( f \) with a feature of the transformed function. \[ \text { domain of }(0, \infty) \] \( h(x)=f(x+3)=3 f(x)-3 \) \( g(x)=-f(x-3) \)

The population of a southern city follows the exponential law. Use this information to answer parts a and b . (a) If N is the population of the city and t is the time in years, express N as a function of t . \( \mathrm{N}(\mathrm{t})= \) (Type an expression using t as the variable and in terms of \( e \).) (b) If the population doubled in size over 19 months and the current population is 50,000 , what will the population be 3 years from now? The population will be approximately \( \square \) people. (Do not round until the final answer. Then round to the nearest whole number as needed.)

Suppose that the function \( h \) is defined on the interval \( (-2,2] \) as follows. \[ h(x)=\left\{\begin{array}{ll}-1 & \text { if }-2<x \leq-1 \\ 0 & \text { if }-1<x \leq 0 \\ 1 & \text { if } 0<x \leq 1 \\ 2 & \text { if } 1<x \leq 2\end{array}\right. \] Find \( h(-1), h(-0.5) \), and \( h(1) \). \( h(-1)=\square \) \( h(-0.5)=\square \)

If \( f(x)=\frac{7}{x+5} \) and \( g(x)=\frac{x+75}{x^{2}-25} \), determine \( (f+g)(x) \) \( \begin{array}{l}(f+g)(x)=\frac{x+82}{x^{2}-25} \\ (f+g)(x)=\frac{x+82}{x+5} \\ (f+g)(x)=\frac{8}{x^{2}-25} \\ (f+g)(x)=\frac{8}{x-5}\end{array} \)

The population of Sasquatch in Salt Lake County was modeled by the function \( P(t)=\frac{400 t}{t+40} \), where \( t=0 \) represents the year 1803 . When were there fewer than 200 Sasquatch in Salt Lake County? Present your answer, to the nearest whole year, in interval notation. There were fewer than 200 Sasquatch in Salt Lake City between the years

\( s \) denotes the length of the arc of a circle of radius \( r \) subtended by the central angle \( \theta \). Find the missing quantity. \( r=40 \) inches, \( \theta=51^{\circ}, \mathrm{s}= \) ? \( \mathrm{s}=\square \) (Type an integer or decimal rounded to three decimal places as needed.)