Mini Exam 9 — Timed Mini Exams

Questions in this quiz (10)

1. The function $$f$$ is given by $$f(x)=3\sin(3x)+2\cos(6x)$$. Using the period of $$f$$, how many complete cycles occur on the interval $$0\le x\le600$$?

   • $$143$$
   • $$286$$
   • $$318$$
   • $$572$$

2. The function $$f$$ is given by $$f(x)=\sin(3x+0.4)$$. The function $$g$$ is defined by $$g(x)=f(x)-0.25$$. What are the zeros of $$g$$ on the interval $$0\le x\le\pi$$?

   • $$0.256\text{ and }1.021$$
   • $$0.524\text{ and }1.308$$
   • $$0.785\text{ and }1.571$$
   • $$0.112,\;1.047,\;2.418$$

3. The figure shows a circle centered at the origin. The length of arc $$PQ$$ is $$6$$ units and the radius is $$5$$. Which expression gives the distance of point $$Q$$ from the $$y$$-axis?

   • $$\cos\left(\frac{6}{5}\right)$$
   • $$\sin\left(\frac{6}{5}\right)$$
   • $$5\cos\left(\frac{6}{5}\right)$$
   • $$5\sin\left(\frac{6}{5}\right)$$

4. The figure shows the graph of the polar function $$r=4\cos(2\theta)$$. If the domain is restricted to $$0\le\theta\le\frac{\pi}{2}$$, which describes the other remaining piece?

   • The portion in Quadrant I from $$E$$ to $$B$$.
   • The portion in Quadrant II from $$E$$ to $$A$$.
   • The portion in Quadrant III from $$E$$ to $$A$$.
   • The portion in Quadrant III from $$E$$ to $$D$$.

5. The figure shows the graph of a trigonometric function $$f$$. Which of the following could be an expression for $$f(x)$$?

   • $$3\cos\left(2\left(x-\frac{\pi}{4}\right)\right)-1$$
   • $$3\cos\left(2\left(x-\frac{\pi}{8}\right)\right)-1$$
   • $$3\sin\left(2\left(x-\frac{\pi}{4}\right)\right)-1$$
   • $$3\sin\left(2\left(x-\frac{\pi}{8}\right)\right)-1$$

6. If the function $$f(x)=\sqrt{x-1}$$ and $$g(x)=\frac{1}{x+3}$$ are combined, which of the following would result in a function with domain $$x\ge1,\ x\ne-3$$?

   • $$\text{i only}$$
   • $$\text{ii only}$$
   • $$\text{i and ii only}$$
   • $$\text{i, ii, and iii}$$

7. Consider the function $$g(x)=x^4+2x^3-5x^2-2x+4$$. If $$2+i$$ is a zero, what is the sum of all real zeros?

   • $$-2$$
   • $$-4$$
   • $$-6$$
   • $$2$$

8. A function $$g(x)=\frac{x+4}{x-1}$$ is a transformation of $$f(x)=\frac{1}{x}$$. Which description correctly matches the transformation?

   • $$\text{Right }1,\ \text{up }1,\ \text{vertical stretch by }5$$
   • $$\text{Left }1,\ \text{up }1,\ \text{vertical stretch by }5$$
   • $$\text{Right }1,\ \text{up }4$$
   • $$\text{Left }1,\ \text{up }4$$

9. Solve the inequality $$\frac{x^2-5x-24}{x-3}\ge0$$.

   • $$(-\infty,-3]\cup(8,\infty)$$
   • $$(-\infty,-3]\cup[8,\infty)$$
   • $$[-3,3)\cup[8,\infty)$$
   • $$(-\infty,-3]\cup(3,8]$$

10. Condense the expression $$5\log_3 x+2\log_3 y-\log_3 z$$ into a single logarithm.

    • $$\log_3\left(\frac{x^5y^2}{z}\right)$$
    • $$\log_3\left(\frac{x^7y^2}{z}\right)$$
    • $$\log_3(x^5y^2z)$$
    • $$\log_3\left(\frac{x^5}{y^2z}\right)$$