Advanced Math: Nonlinear functions — Quiz 4

Questions in this quiz (10)

1. The graph of $$y=f(x)$$ is shown, where $$f(x)=ab^x+c$$, and $$a$$, $$b$$, and $$c$$ are constants. For how many values of $$x$$ does $$f(x)=0$$?

   • $$\text{Three}$$
   • $$\text{Two}$$
   • $$\text{One}$$
   • $$\text{Zero}$$

2. For the function $$f(x)=2x^3-5x^2+4x-3$$, what is the value of $$f(-1)$$?

   • $$-14$$
   • $$-10$$
   • $$10$$
   • $$14$$

3. A social media account has $$2,000$$ followers in January. Each month, the number of followers increases by $$5\%$$ from the previous month. Which equation represents the number of followers $$F$$ after $$m$$ months?

   • $$F=2,000(0.05)^m$$
   • $$F=2,000(1.05)^m$$
   • $$F=2,000(5)^m$$
   • $$F=2,000(1.5)^m$$

4. A ball is thrown upward, and its height is modeled by $$y=-16(x-4)^2+300$$. Which of the following is the best interpretation of the vertex?

   • $$\text{The ball reaches a maximum height of }300\text{ feet after }4\text{ seconds}$$
   • $$\text{The ball reaches a maximum height of }4\text{ feet after }300\text{ seconds}$$
   • $$\text{The ball reaches a minimum height of }300\text{ feet after }4\text{ seconds}$$
   • $$\text{The ball reaches a maximum height of }300\text{ feet after }16\text{ seconds}$$

5. The function $$f(t)=600(0.4)^{t/10}$$ models the intensity of a signal. What is the value of the signal at $$t=0$$?

   • $$600$$
   • $$0.4$$
   • $$10$$
   • $$24$$

6. The function $$g(x)=\frac{x}{a}+8$$, where $$a<0$$. What is the product of $$g(3a)$$ and $$g(5a)$$?

   • 143

7. The area of a rectangle is $$1,200$$ square inches. The length is $$15$$ inches more than the width. Which equation represents this situation?

   • $$0=x^2-15x-1,200$$
   • $$0=x^2+15x-1,200$$
   • $$0=x^2-15x+1,200$$
   • $$0=x^2+15x+1,200$$

8. A collectible card increases in value according to $$V(x)=80(1.04)^x$$, where $$x$$ is the number of years. Which statement best interprets $$V(5)\approx97$$?

   • $$\text{After }5\text{ years, the card is worth about }$97$$
   • $$\text{The card increases by }$97\text{ each year}$$
   • $$\text{The card was originally worth }$97$$
   • $$\text{After }97\text{ years, the card is worth }$5$$

9. The function $$f(x)=(1.44)^{x/2}$$ can be rewritten as $$f(x)=\left(1+\frac{p}{100}\right)^x$$. What is the value of $$p$$?

   • $$20$$
   • $$40$$
   • $$44$$
   • $$144$$

10. The function $$p(x)+25=x^2$$. What is the minimum value of $$p(x)$$?

    • $$-25$$
    • $$0$$
    • $$25$$
    • $$-625$$