Question $1$

$[5]$

Given the function: $g(x)=lo{g}_2(x+4)+1$

$1\mathrm{.}1$ Complete the following table $($correct to two decimal places$).$

$[1]$

$\backslash$table$[[x,-8,-4,-3,-2,0,4],[g(x),,,,,,]]$

$1\mathrm{.}2$ Sketch the of graph $g(x).$ The table in Question $1\mathrm{.}1$ may be of aid to you. You must clearly label all axes and intercepts.

$[2]$

$1\mathrm{.}3$ What is the domain of the function $g(x)?$

$[1]$

$1\mathrm{.}4$ What is the range of the function $g(x)?$

$[1]$

Question $2$

$[7]$

Solve for $x$ :

$2\mathrm{.}1,\frac{3x^2-6x}{x^2-x-2}+\frac{3x}{x^2+x}=5$

$[2]$

Introductory Mathematical Anaiysis A $-$ MAA$00$A$1$ and MAT$00$A$1-$ Exam $-2019$

$-3-$

$2\mathrm{.}210(4^{4x-1})-20=20$

$[2]$

$2\mathrm{.}3log(3x^2-12)=log(x+2)+10$

$[3]$

Question $3$

$[7]$

Differentiate each of the following functions. Do not simplify your answer.

$3\mathrm{.}1,g(x)=(e^x+2)(x^2-5)$

$[2]$

$3\mathrm{.}2f(x)=lo{g}_3(4x^3-9x^2)$

$[2]$

Introductory Mathematical Analysis A $-$ MAA$00$A$1$ and MAT$00$A$1-$ Exam $-2019$

$\mathrm{.}4.$

$3\mathrm{.}3f(x)=\frac{3x^2-2x+1}{3x+5}$

$[3]$

Question $4$

$[5]$

If a company determines that its revenue is given by:

$r=\frac{50q}{\sqrt[\phantom{2}]{100+3q}}$

And that the quantity $(q)$ is defined in terms of number of employees $(m)$ as:

$q=m(2m+1{)}^{\frac{1}{2}}$

$4\mathrm{.}1$ Determine the marginal revenue as a function of $q.$

$[2]$

$4\mathrm{.}2$ Determine the marginal revenue$-$product when the company employs $24$ workers