Basic Technical Mathematics, 11th Edition

CHAPTER 3 REVIEW EXERCISES

CONCEPT CHECK EXERCISES

Determine each of the following as being either true or false. If it is false, explain why.

1. $f(\hspace{0.17em}-\hspace{0.17em}x)\hspace{0.17em}=\hspace{0.17em}\hspace{0.17em}-\hspace{0.17em}f(x)$ for any function f(x).

2. The domain of $f(x)\hspace{0.17em}=\hspace{0.17em}\sqrt{x\hspace{0.17em}-\hspace{0.17em}1}$ is all real numbers $x\hspace{0.17em}>\hspace{0.17em}1.$

3. All points for which $y\hspace{0.17em}>\hspace{0.17em}1$ are in quadrants I and IV.

4. If $y^2\hspace{0.17em}=\hspace{0.17em}x\hspace{0.17em},\hspace{0.17em}$ then y is a function of x.

5. If (2, 0) is an x-intercept of the graph of $y\hspace{0.17em}=\hspace{0.17em}f(x)\hspace{0.17em},\hspace{0.17em}$ then (2, 0) is also an intercept of the graph of $y\hspace{0.17em}=\hspace{0.17em}2f(x)\hspace{0.17em}.\hspace{0.17em}$

6. The graph of $y\hspace{0.17em}=\hspace{0.17em}f(x\hspace{0.17em}+\hspace{0.17em}4)$ is the graph of $y\hspace{0.17em}=\hspace{0.17em}f(x)$ shifted to the left 4 units.

PRACTICE AND APPLICATIONS

In Exercises 7–10, determine the appropriate function.

7. The radius of a circular water wave increases at the rate of 2 m/s. Express the area of the circle as a function of the time t (in s).