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# College Algebra -- Fall 2018 -- midterm

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.
$\bullet$ 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)\$.