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College Algebra -- Fall 2018 -- midterm

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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.

Slopes of lines.png

$\bullet$ 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 $z=g(y)$.