Mini Exam 6 — Timed Mini Exams

Questions in this quiz (10)

1. In the $$xy$$-plane, the function $$f$$ is graphed and contains the point $$(4,3)$$. Which of the following points is on the graph of $$y=3f(x)-2$$?

   • $$(4,3)$$
   • $$(4,7)$$
   • $$(3,4)$$
   • $$(6,3)$$

2. Consider the piecewise function$$P(t)=200-0.5t^2$$, $$0\le t$$<$$10$$$$P(t)=150-5t$$, $$10\le t\le12$$.Which of the following statements is correct about the average rates of change of $$P$$?

   • The average rate of change on $$0\le t\le5$$ is greater than on $$5\le t\le10$$.
   • The average rate of change on $$5\le t\le10$$ is greater than on $$0\le t\le5$$.
   • The average rate of change on $$10\le t\le11$$ is greater than on $$11\le t\le12$$.
   • The average rate of change on $$0\le t\le5$$ equals that on $$5\le t\le10$$.

3. A table of values for a function $$A(x)$$ is shown. A quadratic model is used to fit the data. Which of the following is the best estimate of the maximum value of $$A(x)$$?

   • $$260$$
   • $$295$$
   • $$305$$
   • $$330$$

4. The function $$M$$ is defined by $$M(t)=ae^{-0.02t}+b$$, where $$a$$ and $$b$$ are positive constants. If $$M(0)=20$$ and $$\lim_{t\to\infty}M(t)=4$$, for what value of $$t$$ is $$M(t)=10$$?

   • $$34.66$$
   • $$40.55$$
   • $$45.81$$
   • $$48.96$$

5. Which of the following intervals represents all $$x$$ such that $$p(x)\ge0$$ for $$p(x)=x(x-3)(x+1)$$?

   • $$[-1,3]$$
   • $$(-\infty,-1]\cup[0,3]$$
   • $$(-\infty,-1]\cup[3,\infty)$$
   • $$[-1,0]\cup[3,\infty)$$

6. The function $$f$$ is given by $$f(x)=4\cdot16^x$$. Which of the following is an equivalent form of $$f(x)$$?

   • $$2\cdot4^{2x}$$
   • $$4\cdot2^{4x}$$
   • $$8\cdot2^{2x}$$
   • $$4\cdot4^x$$

7. The function $$f$$ is given by $$f(x)=-3x^5+2x^2-1$$. Which of the following describes the end behavior of $$f$$?

   • $$\lim_{x\to-\infty}f(x)=-\infty\text{ and }\lim_{x\to\infty}f(x)=-\infty$$
   • $$\lim_{x\to-\infty}f(x)=-\infty\text{ and }\lim_{x\to\infty}f(x)=\infty$$
   • $$\lim_{x\to-\infty}f(x)=\infty\text{ and }\lim_{x\to\infty}f(x)=-\infty$$
   • $$\lim_{x\to-\infty}f(x)=-\infty\text{ and }\lim_{x\to\infty}f(x)=\infty$$

8. Let $$a$$ and $$b$$ be positive constants. Which of the following is equivalent to $$3\ln a-2\ln b$$?

   • $$\ln\left(\frac{a^3}{b^2}\right)$$
   • $$\ln(a^3b^2)$$
   • $$\ln(3a-2b)$$
   • $$\ln\left(\frac{3a}{2b}\right)$$

9. The polynomial function $$p$$ is given by $$p(x)=(x-2)(x^2+4x+5)$$. Which of the following describes the zeros of $$p$$?

   • $$p$$ has exactly one real zero and two non-real zeros.
   • $$p$$ has exactly two distinct real zeros.
   • $$p$$ has exactly three distinct real zeros.
   • $$p$$ has no real zeros.

10. In the $$xy$$-plane, the graph of a rational function $$f$$ has a vertical asymptote at $$x=-5$$. Which of the following could be an expression for $$f(x)$$?

    • $$\frac{(x-5)(x+5)}{2(x-5)}$$
    • $$\frac{(x-4)(x+5)}{(x-1)(x+5)}$$
    • $$\frac{(x+1)(x+5)}{(x-5)(x+2)}$$
    • $$\frac{(x-5)(x-3)}{(x-3)(x+5)}$$