Nonlinear Functions 4 — Advanced Math

Questions in this quiz (6)

1. The functions $$f$$ and $$g$$ are defined by the given equations.$$f(t)=4+|t^2-9|$$$$g(x)=x-6+|\frac{x}{x+2}|$$If $$f(5)=d$$, where $$d$$ is a constant, what is the value of $$g(d)$$?

   • $$11$$
   • $$\frac{15}{11}$$
   • $$\frac{164}{11}$$
   • $$\frac{154}{11}$$

2. The height above the ground, $$h$$, in meters, of a projectile $$t$$ seconds after it is launched is modeled by the function:$$h(t)=-3t^2+48t$$What is the maximum height, in meters, that the projectile reaches?

   • $$48$$
   • $$64$$
   • $$192$$
   • $$384$$

3. A quadratic function is defined by $$f(x)=a(x-h)^2+k$$, where $$a$$, $$h$$, and $$k$$ are constants. In the $$xy$$-plane, the graph of $$y=f(x)$$ has its vertex at $$(2,5)$$ and passes through the point $$(6,-3)$$. What is the value of $$a$$?

   • $$-2$$
   • $$-1$$
   • $$-\frac{1}{2}$$
   • $$2$$

4. A company builds custom storage crates, each in the shape of a right rectangular prism. Each crate has a height of $$6$$ inches. The width of each crate's base is $$w$$ inches, and the length is $$w+5$$ inches. Which function $$V$$ gives the volume of each crate, in cubic inches, in terms of $$w$$?

   • $$V(w)=6w(w+5)$$
   • $$V(w)=6w+w+5$$
   • $$V(w)=w(w+5)+6$$
   • $$V(w)=w(w+5)(w+6)$$

5. The function $$f$$ is defined by $$f(x)=a\sqrt{x+b}$$,where $$a$$ and $$b$$ are constants. In the $$xy$$-plane,the graph of $$y=f(x)$$ passes through the point $$(-9,0)$$,and $$f(0)$$ > $$0$$. Which of the following must be true?

   • $$b=-9$$
   • $$b=3$$
   • $$b=-3$$
   • $$b=9$$

6. The table shows the number of bacteria per $$\text{mL}$$ at the end of each day.The number of bacteria in a lab culture is growing at an exponential rate, as shown in the table above. At this rate, on which day would the number of bacteria per $$\text{mL}$$ reach $$4.86\times10^6$$?

   • $$5$$
   • $$6$$
   • $$7$$
   • $$9$$