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?”