Mini Exam 2 — Timed Mini Exams

Questions in this quiz (10)

1. The table gives values for a function $$f$$ at selected values of $$x$$. Which of the following statements is true?

   • $$f$$ is linear because the average rate of change is constant.
   • $$f$$ is quadratic because the first differences are constant.
   • $$f$$ is quadratic because the second differences are constant.
   • $$f$$ is exponential because the ratios are constant.

2. The binomial theorem can be used to expand $$q(x)=(2x-1)^6$$. What is the coefficient of the $$x^4$$ term?

   • $$15·(-1)^2·2^4$$
   • $$20·(-1)^2·2^4$$
   • $$240$$
   • $$20·(-1)^4·2^2$$

3. The table gives polar coordinates $$(r, θ)$$ for four points. Which point lies in Quadrant III?

   • A
   • B
   • C
   • D

4. In the $$xy$$-plane, two different angles α and β are in standard position and share a terminal ray. Which values of $$α$$ and $$β$$ satisfy this?

   • $$α=\frac{π}{2}, β=\frac{7π}{3}$$
   • $$α=\frac{2π}{3}, β=\frac{9π}{5}$$
   • $$α=\frac{3π}{4}, β=\frac{11π}{4}$$
   • $$α=\frac{π}{6}, β=\frac{5π}{6}$$

5. In the $$xy$$-plane, the function k is given by $$k(x)=2^{x-3}$$. Which expression represents $$k(x)$$ as a vertical dilation of $$f(x)=2^x$$?

   • $$(\frac{1}{8})·2^x$$
   • $$8·2^x$$
   • $$2^x - 3$$
   • $$\frac{2^x}{3}$$

6. The function $$f$$ is given by $$f(x)=3\sin(\pi x)-2$$. The graph of $$f$$ is translated horizontally $$\frac{1}{2}$$ unit to the left to form $$g$$. Which of the following is an expression for $$g(x)$$?

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

7. The function $$T$$ models temperature as a function of time $$t$$, and the function $$E$$ models energy usage as a function of temperature. Let $$M(t)=E(T(t))$$. Which of the following best describes $$M$$?

   • Energy usage as a function of time.
   • Temperature as a function of energy usage.
   • Time as a function of temperature.
   • Energy usage as a function of temperature.

8. In the $$xy$$-plane, the graph of which of the following functions has a vertical asymptote at $$x=\frac{5\pi}{6}$$?

   • $$f(x)=\tan x$$
   • $$f(x)=\tan\left(x-\frac{\pi}{3}\right)$$
   • $$f(x)=\tan\left(x-\frac{5\pi}{6}\right)$$
   • $$f(x)=\tan\left(x+\frac{\pi}{6}\right)$$

9. The function $$h$$ is given by $$h(x)=\frac{x^2-9}{(x-3)(x+1)}$$. Which of the following statements about holes in the graph of $$h$$ is true?

   • There is a hole at $$x=3$$ only because the factor cancels completely.
   • There is a hole at $$x=-1$$ only because the factor cancels completely.
   • There are holes at both $$x=3$$ and $$x=-1$$.
   • There are no holes because no factors cancel.

10. A regression model $$R$$ is created for a data set. On the residual plot, point $$C$$ has residual $$2.1$$ and point $$D$$ has residual $$-1.2$$. Which of the following is true?

    • The model underestimates at $$C$$ and overestimates at $$D$$, and the error is larger at $$C$$.
    • The model overestimates at $$C$$ and underestimates at $$D$$, and the error is larger at $$D$$.
    • The model underestimates at $$C$$ and overestimates at $$D$$, and the error is larger at $$D$$.
    • The model overestimates at $$C$$ and underestimates at $$D$$, and the error is larger at $$C$$.