Getting Ready for 5.1 (Combining Functions)

 $R\left(x\right)=\frac{11}{3}x$   represents "reaction distance" of a driver.  This is how long it takes for an "average" person to react and apply his brakes once he recognizes there is a hazard in the road.  R is in feet and x is in miles per hour.  Find R(60) and interpret the result. 

•  $R\left(60\right)=220$  and means that it takes 60 seconds for a person to react when he sees a hazard 220 feet in front of him.

•  $R\left(60\right)=3.67$  and means it takes 3.67 seconds for a person to react when he sees a hazard that is 60 feet in front of him.

•  $R\left(60\right)=220$  and means that when a person is driving 60 mph and sees a hazard, he drives an additional 220 feet before her reacts.

•  $R\left(60\right)=3.67$  and means that when a person is driving 60 mph and sees a hazard, it takes him 3.67 seconds to react.

 $B\left(x\right)=\frac{1}{9}x^2$   represents "braking distance" of a driver. This is the distance that an "average" car travels after the brakes  have been applied.  B is in feet and x is in miles per hour.  Find B(60) and interpret the results.

• B(60)=400 and means when a person is driving 60 mph the braking distance is 400 ft.

• B(60)=44.44 and means that when a person is driving 60 mph the braking distance is 44.44 ft.

• B(60)=400 and means that when a person  sees a hazard 400 feet in front of him it takes him 60 seconds to apply his brakes.

• B(60)=44.44 and means that when a person is going 60 mph it takes him 44.44 seconds to apply his brakes.

For wet, level pavement, highway engineers add a person's reaction distance, R(x), and his braking distance, B(x) to get a new function:  $S\left(x\right)=\frac{x^2}{9}+\frac{11x}{3}$ which is the actual stopping distance . Add these fractions and simplify.

•  $S\left(x\right)=\frac{x^2+11x}{9}$  

•  $S\left(x\right)=\frac{x^2+11x}{27}$  

•  $S\left(x\right)=\frac{x^2+33x}{9}$  

•  $S\left(x\right)=\frac{3x^2+99x}{27}$  

•  $S\left(x\right)=\frac{3x^2+11x}{9}$  

 $S\left(x\right)=\frac{x^2+33x}{9}$ ,  $R\left(x\right)=\frac{11}{3}x$  ,   $B\left(x\right)=\frac{1}{9}x^2$  Using these  formulas for stopping distance, reaction distance and braking distance, where S, R and B are in feet and x is miles per hour, which of these statements is FALSE?

•  $S\left(60\right)=620$  means the stopping distance for  a car traveling 60 mph is 620 feet.

•  $S\left(60\right)=R\left(60\right)+B\left(60\right)$  

•  $S\left(x\right)=R\left(x\right)+B\left(x\right)$  

• If the reaction distance of someone going 60 mph is 220 ft and the braking distance is 400 ft, then the stopping distance will be 620 ft.

•  $S\left(620\right)=R\left(220\right)+B\left(400\right)$  

 $f\left(x\right)=\frac{x+5}{\left(x-3\right)^2}$  Find the domain:

•  $x\ne3,\ x\ne-5$  

•  $x\ne3$  

•  $x\ne0$  

•  $\left(-\infty,\infty\right)$  

Find the domain of : $\sqrt{\left(x-5\right)}$  

•  $x\ne5$  

•  $\left[5,\infty\right)$  

•  $\left(-\infty,-5\right)$  

•  $x\ne\pm5$  

 $\sqrt{\left(x-5\right)^2}$  Find the domain:

•  $x\ne5$  

•  $\left(5,\infty\right)$  

•  $\left(-\infty,\infty\right)$  

•  $\left[5,\infty\right]$  

Find the domain. $f\left(x\right)=x^2-5x-6$  

•  $x\ne6,x\ne-1$  

•  $x\ne-6,\ x\ne1$  

•  $\left(-\infty,\infty\right)$  

•  $x\ne-3,\ x\ne2$  

•  $x\ne3,\ x\ne-2$  

 $f\left(x\right)=\left|x-5\right|$  Find the domain.

•  $\left(-\infty,\infty\right)$  

•  $x\ne5$  

•  $\left[5,\infty\right)$  

•  $\left[-5,5\right]$  

 $f\left(x\right)=The\ cube\ root\ of\ \left(x-8\right)$  Find the domain.

•  $x\ne8$  

•  $\left[8,\infty\right]$  

•  $\left(-\infty,\infty\right)$  

•  $\left(-2,2\right)$