Nonlinear Functions 2 — Advanced Math

Questions in this quiz (10)

1. The graph of the quadratic function $$f$$ is a parabola in the $$xy$$-plane. The vertex of the parabola is at $$(2,-3)$$, and the parabola passes through the point $$(4,5)$$. What is the value of $$f(0)$$?

   • $$-3$$
   • $$1$$
   • $$5$$
   • $$13$$

2. The population of a certain city was $$80000$$ in $$2015$$. The city's population is projected to increase by $$3\%$$ each year after $$2015$$. Which of the following functions models the city's population, $$P(t)$$, as a function of the number of years, $$t$$, after $$2015$$?

   • $$P(t)=0.03(80000)^t$$
   • $$P(t)=1.03(80000)^t$$
   • $$P(t)=80000(0.03)^t$$
   • $$P(t)=80000(1.03)^t$$

3. The profit, $$p(t)$$, in thousands of dollars, for a company $$t$$ months after a new product launch is modeled by the equation:$$p(t)=-2t^2+24t+50$$For which of the following intervals of $$t$$ is the profit $$p(t)$$ strictly increasing?

   • $$2$$ < t < $$5$$
   • $$4$$ < t < $$8$$
   • $$7$$ < t < $$10$$
   • $$9$$ < t < $$12$$

4. The function $$A(t)=500(1.05)^t$$ models the value, in dollars, of an investment $$t$$ years after it was made. How many years does it take for the value of the investment to double?

   • $$1.05$$
   • $$\log(2)$$
   • $$\frac{\log(2)}{\log(1.05)}$$
   • $$\frac{\log(500)}{2}$$

5. A sample of a radioactive substance has an initial mass of $$640$$ grams. The substance has a half-life of $$8$$ years, meaning its mass is reduced by half every $$8$$ years. What will be the mass, in grams, of the sample after $$24$$ years?

   • $$80$$
   • $$160$$
   • $$320$$
   • $$640$$

6. The graph of $$y=h(x)$$ is shown, where the function $$h$$ is a polynomial function. For how many values of $$x$$ does $$h(x)=3$$?

   • $$1$$
   • $$2$$
   • $$3$$
   • $$4$$

7. The function $$f$$ is defined by $$f(x)=b(x-3)(x+1)(x-4)$$, where $$b$$ is a constant. In the $$xy$$-plane, the graph of $$y=f(x)$$ passes through the point $$(0,24)$$. What is the value of $$b$$?

   • $$-2$$
   • $$-1$$
   • $$1$$
   • $$2$$

8. $$f(x)=x^2-11x-60$$If the given function $$f$$ is graphed in the $$xy$$-plane, where $$y=f(x)$$, what is an $$x$$-intercept of the graph?

   • $$(12,0)$$
   • $$(15,0)$$
   • $$(-5,0)$$
   • $$(5,0)$$

9. $$f(x)=|42-2x|$$The function $$f$$ is defined by the given equation. For which of the following values of $$m$$ does $$f(m)=3m$$?

   • $$7$$
   • $$\frac{7}{5}$$
   • $$\frac{42}{5}$$
   • $$\frac{28}{3}$$

10. The function $$f$$ is defined by $$f(x)=x^2-12x+c$$, where $$c$$ is a constant. For a particular value of $$c$$, the value of $$f(6)$$ is at least $$15$$. Which of the following could be the value of $$f(10)$$?

    • $$31$$
    • $$-14$$
    • $$-10$$
    • $$2$$