Attempt the problems below to self-assess topics that need attention. Use paper and pen or pencil and number each item so you may compare with the answers later. Do NOT use a calculator, graphing tool, or AI to assist you. Many of the topics addressed below can be reviewed in Chapter 6 and Chapter 7 below. Return to this pretest after you feel you have made sufficient progress. Answers may be found at the end of this chapter.
The value of a classic car purchased in the year 2000 loses value over time. In 2015 it was worth $19 thousand, while 10 years later it was worth $17 thousand.
Sketch a linear graph with the years since 2000 on the horizontal axis and value of the car in thousands of dollars on the vertical axis. Include the given data points.
Let \(g(x) = \begin{cases}
-x^2+2, & \text{if $x\lt 0$} \\
3, & \text{if $0 \leq x \lt 4$} \\
6-x, & \text{if $x \gt 4$} \\
\end{cases}
\text{.}\) Sketch a graph of \(y=g(x)\text{.}\) Then, evaluate each of the following expressions, if defined.
Describe how the graph of \(y = x^2\) may be transformed to obtain the graph of the function \(f(x) = - (x+3)^2 + 6\text{.}\) Sketch its graph labelling any interesting features. Then algebraically find the zeros of \(f\) and describe their relevance to the graph. State the domain and range of \(f\text{.}\)
Suppose \(f\) is a one-to-one function satisfying \(f(1) = 3\text{,}\)\(f(3) = 1\text{,}\)\(f(-2) = 5\text{,}\) and \(f(0) = -1\text{.}\) Evaluate each of the following expressions, if possible.
