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# College Algebra -- Fall 2018 -- midterm

### From Mathematics Is A Science

**MATH 130 -- Fall 2018 -- Midterm exam**

Name:_________________________ $\qquad$ 7 problems, 10 points each

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

$\bullet$ **1.** Solve the following equations:
$$(a)\ x^2+2x+1=0,\quad (b)\ x^2=-1,\quad (c)\ x^2=1.$$

$\bullet$ **2.** Sketch the graph of the function $f$ given by its list of values below. Is it one-to-one?
$$\begin{array}{r|ll}
x&1&2&3&4&5\\
\hline
y=f(x)&1&2&0&3&1
\end{array}$$

$\bullet$ **3.** Find the implied domain of the function given by the formula:
$$f(x)=\sqrt{x+1}+\sqrt{x-1}.$$

$\bullet$ **4.** Find the domains and the ranges of the three functions the graphs (straight lines) of which are shown below.

$\bullet$ **5.** Provide a formula for the function $y=f(x)$ that represents a parking fee for a stay of $x$ hours. It is computed as follows: free for the first hour and $\$1$ per hour beyond.

$\bullet$ **6.** By transforming the graph of $y=x^2$, plot the graphs of the functions: (a) $y=\sqrt{x}$ and (b) $y=\sqrt{x+3}$.

$\bullet$ **7.** Represent the function $h(x)=(x-1)^2+(x-1)^3$ as the composition $g\circ f$ of two functions $y=f(x)$ and $z=g(y)$.