Free Printable Module 9 quiz review

1.

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

a)

$y=\frac{-4.2}{x}$

y= -.7

b)

$y=-72x$

y=-432

c)

$y=\frac{-72}{x}$

y=-12

d)

$y=-4.2x$

y= -25.2

2.

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

a)

I. Direct, k=1.5

II. Inverse, k= 7.5

III. neither

IV. Inverse, k=3

b)

I. Direct, k=1.5

II. Inverse, k= 7.5

III. Inverse, k=100

IV. Direct, k=3

c)

I. Inverse, k=1.5

II. Direct, k=7.5

III. neither

IV. Inverse, k=3

d)

I. Inverse, k=1.5

II. Direct, k=7.5

III. Inverse, k=100

IV. Inverse, k=3

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.

a)

k=21.875

$y=21.875x$

y=437.5 pounds

b)

k=21.875

$y=\frac{21.875}{x}$

y=1.36 pounds

c)

k=5600

$y=5600x$

y=112000 pounds

d)

k=5600

$y=\frac{5600}{x}$

y=280 pounds

4.

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

a)

$f\left(x\right)=\frac{4}{x-5}-3$

b)

$f\left(x\right)=\frac{4}{x+5}-3$

c)

$f\left(x\right)=\frac{4}{x+3}-5$

d)

$f\left(x\right)=\frac{4}{x-3}-5$

5.

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

a)

Left 1, up 2.

b)

Right 1, up 2

c)

Left 1, down 2

d)

Right 1, down 2

6.

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.

a)

$\left(-\infty,\infty\right)$

b)

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

c)

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

d)

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

7.

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 VA and HA.

State x and y intercepts.

a)

x=-1

y=2

(-3, 0)

(0,6)

b)

x=2

y=-1

(0, -3)

(6,0)

c)

x=4

y=-1

(0, -3)

(0,6)

d)

x=-1

y=2

(0, -3)

(6,0)

8.

Given the rational function below, state the requested information.

$y=\frac{4x+12}{x^2+7x+12}$

Domain

a)

$\left(-\infty,\infty\right)$

b)

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

c)

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

d)

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

9.

Given the rational function below, state the requested information.

$y=\frac{4x+12}{x^2+7x+12}$

Hole, VA and HA

a)

Hole: x= -4

VA: x= -3

HA y=o

b)

Hole: x= -3

VA: x= -4

HA none

c)

Hole: x= -3

VA: x= -4

HA y=o

d)

Hole: x= -4

VA: x= -3

HA none

10.

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.)

a)

$y=x^2-5$

b)

$y=x^2+1$

c)

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

d)

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

11.

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)

Where is the location of the hole?

(Hint: Find the x value of the hole. Then plug that x value in to the simplified equation to find the y value of the hole)

a)

(-5, 26)

b)

(-5, -24)

c)

(5, 26)

d)

(5, -24)

12.

Find the vertical and horizontal asymptotes of the function: $f\left(x\right)=\frac{3x+8}{x+2}$ . State the domain.

a)

Domain: $\left(-\infty,-2\right)U\left(-2,\infty\right)$

VA: x= -2

HA: none

b)

Domain: $\left(-\infty,-2\right)U\left(-2,\infty\right)$

VA: x= 2

HA: y=3

c)

Domain: $\left(-\infty,\infty\right)$

VA: x=2

HA: y=3

d)

Domain: $\left(-\infty,-2\right)U\left(-2,\infty\right)$

VA: x= -2

HA: y=3

13.

Write the equation of the reciprocal function graphed below. The parent function is $f\left(x\right)=\frac{2}{x}$

a)

$f\left(x\right)=\frac{2}{x+2}+3$

b)

$f\left(x\right)=\frac{2}{x-2}-3$

c)

$f\left(x\right)=\frac{2}{x+2}-3$

d)

$f\left(x\right)=\frac{2}{x-2}+3$

14.

Find the vertical asymptote(s) and/or hole(s) for the graph of $f\left(x\right)=\frac{x^2+7x+10}{x^2-2x-8}$ . Then state the domain.

a)

Domain: $\left(-\infty,-2\right)U\left(-2,4\right)U\left(4,\infty\right)$ Hole: x=-2

VA: x=4

b)

Domain: $\left(-\infty,4\right)U\left(4,\infty\right)$

Hole: x=4

VA: none

c)

Domain: $\left(-\infty,-2\right)U\left(-2,\infty\right)$ Hole: none

VA: x=-2

d)

Domain: $\left(-\infty,\infty\right)$

Hole: none

VA: none

Module 9 quiz review

Total questions: 14

Worksheet time: 42mins

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