Nonlinear Functions 1 — Advanced Math

Questions in this quiz (10)

1. The function $$f$$ is defined by $$f(x)=x^3+2$$.What is the value of $$f(3)$$?

   • $$35$$
   • $$17$$
   • $$11$$
   • $$29$$

2. The function $$f(x)$$ is defined by$$f(x)=-3(x-2)^2+5$$.What is the maximum value of $$f(x)$$?

   • $$-3$$
   • $$2$$
   • $$5$$
   • $$7$$

3. The height above the ground of a model rocket, $$h$$, in meters, can be modeled by the equation$$h(t)=-4t^2+32t+64$$where $$t$$ is the time in seconds after launch. What is the maximum height, in meters, that the rocket reaches?

   • $$64$$
   • $$96$$
   • $$128$$
   • $$144$$

4. If $$f(x)=x^2-6x+5$$ and $$g(x)=4x+1$$, for which value of $$x$$ will $$f(x)=g(x)$$?

   • $$-5,5$$
   • $$5+\sqrt{21},5-\sqrt{21}$$
   • $$-\frac{1}{4},\frac{1}{4}$$
   • $$-\sqrt{6},\sqrt{6}$$

5. The area $$A$$, in square meters, of a rectangular garden can be represented by the expression$$x(x+4)$$, where $$x$$ is the length, in meters, of the garden.Which expression represents the width, in meters, of the garden?

   • $$4$$
   • $$x$$
   • $$x+4$$
   • $$x(x+4)$$

6. $$f(t)=2500(0.92)^t$$The function $$f$$ models the number of discount coupons a store gives out each year,where $$t$$ represents the number of years since the end of $$2015$$ and $$0\le t\le5$$.If $$y=f(t)$$ is graphed in the $$ty$$-plane, which of the following is the best interpretationof the $$y$$-intercept of the graph in this context?

   • The minimum estimated number of coupons given out during the $$5$$ years was $$2500$$.
   • The estimated number of coupons given out at the end of $$2015$$ was $$2500$$.
   • The estimated number of coupons given out at the end of $$2015$$ was $$1840$$.
   • The minimum estimated number of coupons given out during the $$5$$ years was $$1840$$.

7. $$y=64^{(2x-3)}$$The graph of the given equation in the $$xy$$-plane has a $$y$$-intercept of $$(a,b)$$. Which ois the value of b?

   • $$\frac{1}{64^{-3}}$$
   • $$64^3$$
   • $$\frac{1}{64^3}$$
   • $$64$$

8. The height $$h$$, in meters, of a model rocket $$t$$ seconds after it is launched can be modeled by the function$$h(t)=-t^2+12t+5$$The rocket reaches a height of $$29$$ meters twice, once on its way up and once on its way down. What is the positive difference, in seconds, between the two times the rocket reaches a height of $$29$$ meters?

   • $$3$$
   • $$4$$
   • $$6$$
   • $$4\sqrt{3}$$

9. $$c(t)=150(0.8)^t$$The function $$c$$ models the amount of a chemical, in grams, remaining in a container $$t$$ hours after a reaction begins. According to the model, what is the amount of the chemical, in grams, immediately when the reaction begins?

   • $$30$$
   • $$80$$
   • $$120$$
   • $$150$$

10. A company models its weekly profit $$P$$, in thousands of dollars, for a new product using the function$$P(t)=-t^2+10t+36$$where $$t$$ represents the number of weeks since launch. What was the company's profit at the time of launch?

    • $$18,000$$
    • $$36,000$$
    • $$46,000$$
    • $$72,000$$