Mini Exam 7 — Timed Mini Exams

Questions in this quiz (10)

1. The table shows values of an exponential function $$f(x)=ab^x$$. Which of the following statements is true?

   • $$f$$ demonstrates exponential decay because $$0$$<$$b$$<$$1$$
   • $$f$$ demonstrates exponential growth because $$b$$>$$1$$.
   • $$f$$ is linear because the differences are constant.
   • $$f$$ is quadratic because second differences are constant.

2. The function $$f$$ is given by $$f(x)=x^2-4$$, and the function $$g$$ is given by $$g(x)=\frac{x+2}{x}$$. Which of the following is an expression for $$f(g(x))$$?

   • $$\left(\frac{x+2}{x}\right)^2-4$$
   • $$\frac{x^2+4}{x^2}$$
   • $$\frac{x^2}{x^2-4}$$
   • $$\frac{x^2+2x-4}{x}$$

3. The function $$g$$ is given by $$g(x)=5\sin(2x)$$. Which of the following is an equivalent form of $$g(x)$$?

   • $$10\sin x\cos x$$
   • $$5\cos^2x-5\sin^2x$$
   • $$5-10\sin^2x$$
   • $$5\sin x\cos x$$

4. A complex number has rectangular coordinates $$(-2,2\sqrt{3})$$. Which of the following represents the number in polar form?

   • $$4\left(\cos\frac{2\pi}{3}+i\sin\frac{2\pi}{3}\right)$$
   • $$2\left(\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\right)$$
   • $$4\left(\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\right)$$
   • $$2\left(\cos\frac{2\pi}{3}+i\sin\frac{2\pi}{3}\right)$$

5. The function $$f$$ is given by $$f(x)=2x^2-3x+1$$. Which of the following represents the graph of $$f$$ after a vertical dilation by a factor of $$3$$?

   • $$6x^2-9x+3$$
   • $$2(3x)^2-3(3x)+1$$
   • $$2x^2-3x+3$$
   • $$6x^2-3x+1$$

6. The functions $$f$$ and $$g$$ are defined for all real numbers such that $$g(x)=f(3(x+2))$$. Which of the following sequences of transformations maps the graph of $$f$$ to the graph of $$g$$ in the same $$xy$$-plane?

   • A horizontal dilation by a factor of $$3$$, followed by a translation left $$2$$ units.
   • A horizontal dilation by a factor of $$\frac{1}{3}$$, followed by a translation right $$2$$ units.
   • A horizontal dilation by a factor of $$\frac{1}{3}$$, followed by a translation left $$2$$ units.
   • A horizontal dilation by a factor of $$3$$, followed by a translation right $$2$$ units.

7. Let $$f$$ be a rational function. The numerator has a zero at $$x=2$$ but not at $$x=-3$$. The denominator has zeros at both $$x=2$$ and $$x=-3$$. The multiplicities at $$x=2$$ are equal in numerator and denominator. Which of the following is true?

   • The graph has holes at both $$x=2$$ and $$x=-3$$.
   • The graph has a vertical asymptote at $$x=2$$ and a hole at $$x=-3$$.
   • The graph has a hole at $$x=2$$ and a vertical asymptote at $$x=-3$$.
   • The graph has vertical asymptotes at both $$x=2$$ and $$x=-3$$.

8. The table shows values of a function $$P(t)$$. Which model best fits the data?

   • $$y=5+5t$$
   • $$y=5(2)^t$$
   • $$y=5(1.5)^t$$
   • $$y=5t^2$$

9. The polynomial $$k(x)=ax^4+bx^3-6$$ has real coefficients. One zero is $$1+i$$. Another zero is $$2$$. Each zero has multiplicity $$1$$. Which of the following must be true?

   • $$1-i$$ is also a zero.
   • The graph has exactly two $$x$$-intercepts.
   • All zeros are real.
   • The polynomial has degree $$3$$.

10. Consider the functions $$f(x)=\log_5(x-2)+\log_5(x+1)$$ and $$g(x)=\log_5(x+3)$$. What are all $$x$$-values where the graphs intersect?

    • $$x=1$$ only
    • $$x=4$$ only
    • $$x=-3$$ and $$x=1$$
    • $$x=1+\sqrt{6}$$ only