Mini Exam 1 — Timed Mini Exams

Questions in this quiz (10)

1. Consider the functions $$g(x)=8^{x-1}$$ and $$h(x)=2^{3x+5}$$ Find the $$x$$-coordinate of their intersection.

   • $$-4$$
   • No Solution
   • $$0$$
   • $$2$$

2. The function is given by $$f(x)=\\log_3(2x-1)$$ Find the value of $$x$$ such that $$f(x)=4$$.

   • $$\\frac{41}{2}$$
   • $$41$$
   • $$82$$
   • $$\\frac{82}{2}$$

3. The function is $$k(\\theta)=3\\sin(2\\theta)$$ Find all values of $$\\theta$$ in $$[0,2\\pi)$$ such that $$k(\\theta)=-\\frac{3}{2}$$.

   • $$\\frac{\\pi}{6},\\frac{5\\pi}{6}$$
   • $$\\frac{7\\pi}{12},\\frac{11\\pi}{12}$$
   • $$\\frac{\\pi}{12},\\frac{7\\pi}{12}$$
   • $$\\frac{5\\pi}{12},\\frac{11\\pi}{12}$$

4. Which expression is equivalent to $$\\log_5(x^8y^2)$$?

   • $$8\\log_5 x+2\\log_5 y$$
   • $$\\log_5 x^8+\\log_5 y$$
   • $$10\\log_5(xy)$$
   • $$4\\log_5 x+\\log_5 y^2$$

5. In the $$xy$$-plane, the graph of a rational function $$f$$ has a hole at $$x=3$$. Input values of $$f$$ sufficiently close to $$3$$ correspond to output values arbitrarily close to $$5$$. Which of the following could define $$f(x)$$?

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

6. At time $$t=0$$, the population of a town is $$18{,}500$$. Each year, the population decreases by $$3\\%$$. Which of the following models the population $$P(t)$$ after $$t$$ years?

   • $$P(t)=18500-0.03t$$
   • $$P(t)=18500(0.97)^t$$
   • $$P(t)=18500(1.03)^t$$
   • $$P(t)=18500-0.97t$$

7. Where both expressions are defined, which of the following is equivalent to $$\\frac{\\csc^2 x-1}{\\csc^2 x}$$?

   • $$\\frac{\\cos^2 x}{\\sin^2 x}$$
   • $$\\tan^2 x$$
   • $$\\cos^2 x$$
   • $$\\sin^2 x$$

8. The location of a point in polar coordinates is $$\\left(2,\\frac{7\\pi}{6}\\right)$$ Which of the following represents its rectangular coordinates $$(x,y)$$?

   • $$(-\\sqrt{3},-1)$$
   • $$(-1,-\\sqrt{3})$$
   • $$(-\\sqrt{3},1)$$
   • $$(1,-\\sqrt{3})$$

9. Which of the following statements is true about the exponential function $$h(x)=-5(0.5)^x$$?

   • h is increasing, and the graph is concave up.
   • h is decreasing, and the graph is concave down.
   • h is increasing, and the graph is concave down.
   • h is decreasing, and the graph is concave up.

10. The function $$f(t)=e^{2t}$$ and $$g(t)=\\ln(3t)$$. If $$h(t)=(f\\circ g)(t)$$ for $$t>0$$, which expression represents $$h(t)$$?

    • $$3t^2$$
    • $$3t^2$$
    • $$e^{2\\ln(3t)}$$
    • $$9t^2$$