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# College Algebra -- Fall 2016 -- final exam

**MATH 130 -- Fall 2016 -- final exam**

Name:_________________________ $\qquad$ 10 problems, 100 points total

- Write the problems in the given order, each problem on a separate page.
- Show enough work to justify your answers.

$\bullet$ **1.** Solve the following equation: $\sqrt{x^2-7}-3=0$.

$\bullet$ **2.** A sketch of the graph of a function $f$ and its table of values are given below. Complete the table:
$$\begin{array}{r|ll}
x&0& &3& &1\\
\hline
f(x)&2&1& &5&
\end{array}$$

$\bullet$ **3.** Find the implied domain of the function given by:
$$\frac{1}{\sqrt{x+1}}.$$

$\bullet$ **4.** Three straight lines are shown below. Find their slopes:

$\bullet$ **5.** Half of the graph of an odd function is shown below; provide the other half:

$\bullet$ **6.** By transforming the graph of $y=e^x$, plot the graph of the function $f(x)=-e^{x+3}$. Identify the domain, the range, and the asymptotes.

$\bullet$ **7.** The population of a city has doubled in $10$ years. Assuming exponential growth, how much does it grow every year?

$\bullet$ **8.** Solve the equation: $3^x=3^{x+1}$.

$\bullet$ **9.** Solve the system of linear equations and geometrically represent its solution:
$$\begin{cases}
x-2y&=1,\\
x+2y&=-1.
\end{cases}$$

$\bullet$ **10.** Set up, do not solve, the system of linear equations for the following problem: “One serving of tomato soup contains $100$ Cal and $18$ g of carbohydrates. One slice of whole bread contains $70$ Cal and $13$ g of carbohydrates. How many servings of each should be required to obtain $230$ Cal and $42$ g of carbohydrates?”