Average Rate of Change & Long Division

The table below gives the number of fish in a local koi pond each year.

What is the average rate of change from 2 to 5 years?

• 24 more fish each year

• 72 more fish each year

• 20.4 more fish each year

• 15 more fish each year

Tags

CCSS.HSF.IF.B.6

A car rental company charges an initial fee plus a constant fee per kilometer driven. The table compares the total distance driven on the trip (in kilometers) and the price of the rental (in dollars).

What is the average rate of change between 110 km and 145 km?

• $0.60 per km

• $1.67 per km

• $21 per km

• $6 per km

Tags

CCSS.HSF.IF.B.6

CCSS.HSS.ID.C.7

Hanna throws a ball off a bridge into a river below. The ball's height above the water in meters, h(t), after t seconds is given by the following function:

 $h\left(t\right)=-2t^2+34$  .
Determine the average rate of change between the first 4 seconds.

• -32 meters per second

• -8 meters per second

• -4 meters per second

• -10 meters per second

Tags

CCSS.HSF.IF.B.6

The graph shows the number of computers that have been infected with a virus, c(d), d days after the computer virus was first reported.

What is the average rate of change between 3 and 5 days?

• 96 computers per day

• 64 computers per day

• 192 computers per day

• 32 computers per day

Tags

CCSS.HSF.IF.B.6

Select all intervals where there is a negative average rate of change.

•  $-2\le x\le-1$  

•  $-1\le x\le1$  

•  $1\le x\le2$  

•  $2\le x\le3$  

•  $-2\le x\le1$  

Given

 $x+4$ is a factor, factor  $x^3+7x^2+21x+36$ .

•  $\left(x+4\right)\left(x^2+3x+11\right)$  

•  $\left(x+4\right)\left(x^2+7x-15\right)$  

•  $\left(x+4\right)\left(x^2+3x+9\right)$  

•  $\left(x+4\right)\left(x^2+7x-3\right)$  

Given

 $x=1$ is a zero, factor  $x^4-8x^2+3x+4$ .

•  $\left(x-1\right)\left(x^3+x^2-7x-4\right)$  

•  $\left(x-1\right)\left(x^3-x^2-7x-4\right)$  

•  $\left(x-1\right)\left(x^3+x^2-9x-6\right)$  

•  $\left(x-1\right)\left(x^3+x^2-8x+4\right)$  

Given $x-3$ is a factor, factor  $x^4+3x^3-13x^2-15x$ .

•  $\left(x-3\right)\left(x^3+3x^2-4x-3\right)$  

•  $\left(x-3\right)\left(x^3+3x^2-4x\right)$  

•  $\left(x-3\right)\left(x^3+6x^2+5x+1\right)$  

•  $\left(x-3\right)\left(x^3+6x^2+5x\right)$  

Given $x=-5$  is a zero, factor  $x^3+9x^2+23x+15$ .

•  $\left(x+5\right)\left(x^2+4x+3\right)$  

•  $\left(x-5\right)\left(x^2+4x+3\right)$  

•  $\left(x+5\right)\left(x^2+9x+15\right)$  

•  $\left(x-5\right)\left(x^2+9x+15\right)$  

Given $2x+3$ is a factor, factor  $4x^3-9x$ .

•  $\left(2x+3\right)\left(2x^2-3\right)$  

•  $\left(2x+3\right)\left(2x^2-3x\right)$  

•  $\left(2x+3\right)\left(2x^2-6x\right)$  

•  $\left(2x+3\right)\left(2x^2-6\right)$