Module 9 quiz review

The variables x and y vary inversely. Use the given values x= -4 and y= 18 to calculate the constant of variation and write the equation. Then find the value of y  when  x=6

State if the tables show direct variation, inverse variation or neither.  State the constant if there is one.

• I. Direct, k=1.5

  II. Inverse, k= 7.5

  III. neither

  IV. Inverse, k=3

• I. Direct, k=1.5

  II. Inverse, k= 7.5

  III. Inverse, k=100

  IV. Direct, k=3

• I. Inverse, k=1.5

  II. Direct, k=7.5

  III. neither

  IV. Inverse, k=3

• I. Inverse, k=1.5

  II. Direct, k=7.5

  III. Inverse, k=100

  IV. Inverse, k=3

The maximum load L of a horizontal beam varies inversely as the distance d between its supports. A beam with 16 feet between its supports has a maximum load of 350 pounds. What is the maximum load of the beam if it has 20 feet between its supports?

Find k. Write the equation. Solve.

Given the reciprocal function:  $f\left(x\right)=\frac{4}{x}$  , write an equation with asymptotes of x= -5 and y= -3.

•  $f\left(x\right)=\frac{4}{x-5}-3$ 

•  $f\left(x\right)=\frac{4}{x+5}-3$ 

•  $f\left(x\right)=\frac{4}{x+3}-5$ 

•  $f\left(x\right)=\frac{4}{x-3}-5$ 

• Left 1, up 2.

• Right 1, up 2

• Left 1, down 2

• Right 1, down 2

The graph of  $g\left(x\right)=\frac{4}{x+1}+2$ , is transformed from the function  $f\left(x\right)=\frac{4}{x}$  State domain. 

•  $\left(-\infty,\infty\right)$ 

•  $\left(-\infty,\ -1\right)U\left(-1,\ \infty\right)$ 

•  $\left(-\infty,\ -1\right)U\ \left(-1,\ 2\right)U\ \left(2,\ \infty\right)$ 

•  $\left(-\infty,2\right)U\left(2,\ \infty\right)$  

• x=-1

  y=2

  (-3, 0)

  (0,6)

• x=2

  y=-1

  (0, -3)

  (6,0)

• x=4

  y=-1

  (0, -3)

  (0,6)

• x=-1

  y=2

  (0, -3)

  (6,0)

Given the rational function below, state the requested information.

 $y=\frac{4x+12}{x^2+7x+12}$ 

Domain

•  $\left(-\infty,\infty\right)$ 

•  $\left(-\infty,\ -3\right)U\left(-3,\infty\right)$ 

•  $\left(-\infty,\ -4\right)U\left(-4,\infty\right)$ 

•  $\left(-\infty,\ -4\right)U\ \left(-4,\ -3\right)U\ \left(-3,\infty\right)$ 

• Hole: x= -4

  VA: x= -3

  HA y=o

• Hole: x= -3

  VA: x= -4

  HA none

• Hole: x= -3

  VA: x= -4

  HA y=o

• Hole: x= -4

  VA: x= -3

  HA none

The graph of the rational function  $f\left(x\right)=\frac{x^3+5x^2+x+5}{x+5}$  is a parabola with a hole in it. (Hint: Factor first)

 

What is the equation of the parabola? (Hint: It is quadratic.)

•  $y=x^2-5$ 

•  $y=x^2+1$ 

•  $y=\left(x^2+1\right)\left(x+5\right)$ 

•  $y=\left(x+1\right)\left(x-1\right)$