Advanced Math: Nonlinear functions — Quiz 2

Questions in this quiz (10)

1. The graph shown gives the estimated value, in dollars, of a tablet as a function of the number of months since it was purchased. What is the best interpretation of the $$y$$-intercept of the graph in this context?

   • $$\text{The estimated value of the tablet was }225\text{ dollars when it was purchased.}$$
   • $$\text{The estimated value of the tablet }24\text{ months after it was purchased was }225\text{ dollars.}$$
   • $$\text{The estimated value of the tablet had decreased by }225\text{ dollars in the }24\text{ months after it was purchased.}$$
   • $$\text{The estimated value of the tablet decreased by approximately }2.25\%\text{ each year after it was purchased.}$$

2. What is the $$y$$-coordinate of the $$y$$-intercept of the graph shown?

   • 3

3. A town has a population of $$20,000$$ in $$2010$$. Each year for the next $$4$$ years, the population increases by $$3\%$$ of the previous year's population. Which equation best models this situation, where $$p$$ is the population and $$x$$ is the number of years after $$2010$$?

   • $$p=20,000(0.97)^x$$
   • $$p=20,000(1.03)^x$$
   • $$p=1.03(20,000)^x$$
   • $$p=20,000+0.03x$$

4. The function $$f$$ is defined by $$f(x)=5x^3$$. The graph of $$y=g(x)$$ is obtained by shifting the graph of $$y=f(x)$$ up $$4$$ units. Which equation defines $$g(x)$$?

   • $$g(x)=5x^3-4$$
   • $$g(x)=5x^3+4$$
   • $$g(x)=5(x+4)^3$$
   • $$g(x)=5x^3\cdot4$$

5. The number of bacteria in a culture triples every hour. Initially, there are $$6,000$$ bacteria. Which equation represents the number of bacteria $$y$$ after $$t$$ hours?

   • $$y=6,000(3)^t$$
   • $$y=3(6,000)^t$$
   • $$y=6,000+t^3$$
   • $$y=6,000(1.03)^t$$

6. The graph of $$y=x^2+12$$ has a $$y$$-intercept at $$(0,y)$$. What is the value of $$y$$?

   • 12

7. The function $$f(x)=150,000(1.10)^x$$ models revenue, in dollars, $$x$$ years after a company launches a product. What is the best interpretation of the statement $$f(3)\approx199,650$$?

   • $$\text{After }3\text{ years after launch, the revenue is approximately }199,650\text{ dollars.}$$
   • $$\text{The revenue increases by }199,650\text{ dollars each year.}$$
   • $$\text{After }199,650\text{ years, the revenue is }3\text{ dollars.}$$
   • $$\text{The revenue is multiplied by }3\text{ each year.}$$

8. In the $$xy$$-plane, the $$y$$-coordinate of the $$y$$-intercept of the graph of $$y=f(x)$$ is $$k$$. Which of the following must be equal to $$k$$?

   • $$f(0)$$
   • $$f(1)$$
   • $$f(-1)$$
   • $$f(2)$$

9. The function $$f(x)=6\sqrt{x}$$. For what value of $$x$$ does $$f(x)=30$$?

   • 25

10. If $$f(x)=\frac{x^2-4x+1}{x-1}$$, what is the value of $$f(2)$$?

    • -3