Functions — Quiz 4

Questions in this quiz (10)

1. If $$f(x)=\frac{1}{x^2}$$, what is $$f(x+h)-f(x)$$?

   • $$\frac{-h}{(x+h)^2x^2}$$
   • $$\frac{-h}{(x+h)^2}$$
   • $$\frac{-h(2x+h)}{(x+h)^2x^2}$$
   • $$\frac{(2x+h)}{(x+h)^2x^2}$$

2. If $$f(x)=kx+m$$, what is $$f^{-1}(x)$$?

   • $$\frac{x}{mk}$$
   • $$\frac{x-m}{k}$$
   • $$\frac{x-m}{km}$$
   • $$\frac{x+k}{m}$$

3. Which of these is the value of the x-coordinate of the intersection point of the graphs of $$y=e^{x+4}$$ and $$y=200$$?

   • $$\ln(200)-4$$
   • $$\ln(200)-8$$
   • $$\ln(200)-6$$
   • $$\ln(200)-10$$

4. What are the vertical and horizontal asymptotes of the rational function: $$y=\frac{7x^2+4}{6x^2-5}$$

   • H: $$y=\frac{7}{6}$$, V: $$x=\pm\sqrt{\frac{5}{6}}$$
   • H: $$y=\frac{7}{5}$$, V: $$x=\pm\sqrt{\frac{5}{6}}$$
   • H: $$y=\frac{7}{6}$$, V: $$x=\pm \sqrt{\frac{6}{5}}$$
   • H: $$y=\frac{5}{6}$$,V: $$x=\pm\sqrt{\frac{5}{6}}$$

5. If $$c$$ and $$d$$ are real, what value(s) are all the real numbers NOT in the domain of $$y=\frac{x-c}{x^2-d^2}?$$

   • $${d}$$
   • $${d,-d,-c}$$
   • $${d,-d}$$
   • $${-c,-d}$$

6. Which of these is the domain of $$\sqrt{(x-10)^9}$$?

   • $$[10, \infty)$$
   • $$(10, \infty)$$
   • $$(-\infty, 10]$$
   • $$[90, \infty)$$

7. Which of these is the domain of $$\sqrt{x^3 - 27}$$?

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

8. If $$f(x) = x^2 - 5x + b$$ passes through the point $$(4, 6)$$, what is $$f(10)$$?

   • 63
   • 60
   • 65
   • 70

9. What is the minimum value of $$f(x)=|(x-a)^2+b|-c$$ for each set of positive real numbers $$a, b,$$ and $$c$$?

   • $$a-b$$
   • $$b+a$$
   • $$-b+a$$
   • $$b-c$$

10. The exponential function $$f(x) = a^x - b$$ passes through the points $$(k, 15)$$ and $$(2k, 240)$$. What is a possible value of $$b$$?

    • $$b = \frac{\sqrt{901} - 29}{2}$$
    • $$b = \frac{\sqrt{901} - 1}{2}$$
    • $$b = \frac{\sqrt{901} +1}{2}$$
    • $$b = \frac{-\sqrt{901} - 1}{2}$$