The exponential function given by \( \mathrm{H}(\mathrm{t}=80,038.18(1.0484) \), where \( t \) is the number of years after 2012, can be used to project the number of centenarians in a certain country. Use this function to project the centenarian population in this country in 2016 and in 2043 . The centenarian population in 2016 is approximately (Round to the nearest whole number.)

Given: \( f(x)=2\left(x^{2}-1\right) \) Sketch function \( f \) on the diagram sheet. Clearly show all intercepts with the axes.

Given \( f(x)=\frac{-2}{x}-2 \), Answer the following questions: .1 Write down the equations of the asymptotes of \( f(x) \). 2 Draw a neat sketch graph of \( f(x) \), clearly indicate the asymptotes and the intercepts with the axes. .3 Write down the domain and range of \( f(x) \).

Find the function that is finally graphed after the following transformations are applied to the graph of \( y=\sqrt{x} \) in the order listed. (1) Shift up 7 units (2) Reflect about the \( x \)-axis (3) Reflect about the \( y \)-axis \( y= \)

Let \( P=(x, y) \) be a point on the graph of \( y=x^{2}-2 \). Complete parts (a) through (e) below. (a) Express the distance \( d \) from \( P \) to the origin as a function of \( x \). \( d(x)= \) (Simplify your answer. Type an exact answer, using radicals as needed.)

(a) Express the distance \( d \) from \( P \) to the origin as a function of \( x \). \( d(x)=\sqrt{x^{4}-3 x^{2}+4} \) (Simplify your answer. Type an exact answer, using radicals as needed.) (b) What is \( d \) if \( x=0 \) ? If \( x=0 \), the distance \( d \) is 2 . (Type an integer or decimal rounded to two decimal placels as needed.) (c) What is \( d \) if \( x=1 \) ? If \( x=1 \), the distance \( d \) is \( \square \). (Type an integer or decimal rounded to two decimal places as needed.)