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Graph of Inverse Function Worksheet

Graph of Inverse Function Worksheet
  • Page 1
 1.  
The weight (w) of the soccer ball used by the age group 8 to 12, vary from 373 grams to 403 grams, inclusive. Write an absolute value inequality describing the weights of soccer balls that are outside the acceptable range.
a.
| w - 403 | < 373
b.
| w - 388 | < 15
c.
| w - 388 | > 15
d.
w < 373 or w > 403


Solution:

w be the weight of a soccer ball, then 373 ≤ w ≤ 403
[Weight of a soccer ball vary from 373 grams to 403 grams, inclusive.]

w < 373 or w > 403
[Outside the acceptable range.]

w < 388 - 15 or w > 388 + 15
[Average of 373 and 403 is 388.]

w - 388 < - 15 or w - 388 > 15
[Rearrange the terms.]

- (w - 388) > 15 or (w - 388) > 15
[If a < - b then - a > b.]

| w - 388 | > 15
[Use: if - x > a or x > a, then | x | > a.]


Correct answer : (3)
 2.  
Earth is not a perfect sphere, but nearly so, with the approximate surface area 510926783 km2. Find the earth's diameter approximately. (Use π = 3.14)
a.
7198 km
b.
12756 km
c.
6378 km
d.
3189 km


Solution:

Surface area of a sphere, S = 4πr2, where r is the radius of the sphere.

d = 2r = 2s4π = sπ

d = 5109267833.14 12756 km.

So, the diameter of the Earth approximately is 12756 km.


Correct answer : (2)
 3.  
The diameter of a tennis ball is between 6.34 cm and 6.68 cm. Write an absolute value inequality that describes the diameter (d) range of a tennis ball.
a.
6.34 < d < 6.68
b.
| d - 6.51 | > 0.17
c.
| d - 6.51 | < 0.17
d.
| d - 6.68 | < 6.34


Solution:

Let d be the diameter of a tennis ball, then 6.34 < d < 6.68
[Diameter of a tennis ball vary from 6.34 cm to 6.68 cm.]

6.34 - 6.51 < d - 6.51 < 6.68 - 6.51
[Average of 6.34 and 6.68 is 6.51.]

- 0.17 < d - 6.51 < 0.17
[Simplify.]

| d - 6.51 | < 0.17
[If - a < ( x - k ) < a, then | x - k | < a.]


Correct answer : (3)
 4.  
A rectangular gift box with volume (V) 968 cm3 and a height of h cm has a square base. Write an equation to find the length of one side of the base and find the value of it for h = 8 cm.
a.
Vh ; 11 cm
b.
Vh ; 88 cm
c.
Vh ; 6.2 cm
d.
Vh ; 121 cm


Solution:

Volume of the rectangular gift box, V = base area × height

Let x be the base length of a rectangular gift box.

V = x2h x2 = Vh
[Base area = x × x = x2.]

So, x = Vh

x = 9688 = 11
[Replace V = 968 cm3 and h = 8 cm.]

So, the length of the one side of the base of a rectangular gift box is 11 cm.


Correct answer : (1)
 5.  
The manufacturer of a particular equipment for fitness, claims that the reduction in weight (w) resulting by using this equipment satisfies the inequality | w - 18 | ≤ 10. Find the maximum weight in pounds reduced by using that equipment as claimed by the manufacturer.
a.
18 pounds
b.
28 pounds
c.
10 pounds
d.
180 pounds


Solution:

| w - 18 | ≤ 10
[Weight reduction inequality.]

- 10 ≤ (w - 18) ≤ 10
[If | x | ≤ a then - axa.]

- 10 + 18 ≤ w ≤ 10 + 18
[Add 18 to each term of the inequality.]

8 ≤ w ≤ 28
[Simplify.]

So, the maximum weight reduced by using the equipment is 28 pounds.


Correct answer : (2)
 6.  
Find the equation of the inverse of y = 2x.
a.
y = - 2x
b.
y = 1 2x
c.
x = 1 2y
d.
y = - 1 2x


Solution:

y = 2x

x = 2y
[Interchange x and y.]

y = x2
[Solve for y.]

So, the equation of the inverse is y = 1 / 2x.


Correct answer : (2)
 7.  
Find the equation of the inverse of y = x - 2.
a.
x = y + 2
b.
x = y - 2
c.
y = x - 2
d.
y = x + 2


Solution:

y = x - 2

x = y - 2
[Interchange x and y.]

y = x + 2
[Solve for y.]

So, the equation of the inverse is y = x + 2.


Correct answer : (4)
 8.  
Find the equation of the inverse of f(x) = x + 23.
[Hint: Replace f(x) with y]
a.
y = - 2x + 3
b.
y = 3x - 2
c.
x = y + 23
d.
Inverse does not exist


Solution:

f(x) = x + 23

y = x + 23
[Replace f(x) by y.]

x = y + 23
[Interchange x and y.]

y = 3x - 2
[Solve for y.]

So, the equation of the inverse is y = 3x - 2.


Correct answer : (2)
 9.  
Find the equation of the inverse of y = 1 7 x2.
a.
y = ± 7x
b.
x = 1 7y
c.
y = - 7x
d.
y = 7x


Solution:

y = 1 / 7x2

x = 1 / 7y2
[Interchange x and y.]

7x = y2
[Multiply throughout by 7.]

y = ± 7x
[Solve for y.]

So, the equation of the inverse is y = ± 7x.


Correct answer : (1)
 10.  
Find the equation of the inverse of y = x2 - 6.
a.
y = ± x + 6
b.
y = - x + 6 only
c.
y = x + 6 only
d.
x2 = y² - 6


Solution:

y = x² - 6

x = y² - 6
[Interchange x and y.]

x + 6 = y²
[Add 6 to both sides of the equation.]

y = ± x + 6
[Solve for y.]

So, the equation of the inverse is y = ± x + 6.


Correct answer : (1)

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