Determine the range of the function modeled by the equation. In late August, Ellis is given some stamps by his uncle. On September 1, he begins to buy new stamps to add to his collection. The number of stamps in his collection can be determined using the equation f(x)=40x+57

Question

, in which x indicates the number of weeks that have gone by since September 1 and f(x)
represents the total number of stamps in his collection. However, Ellis loses interest in his collection after five weeks and stops purchasing new stamps, invalidating the ability of the function to describe the number of stamps he has after that point. How can the range of this real-world function be described using inequality symbols?(1 point)
Responses

57<y<257
57 less than y less than 257

40<y<57
40 less than y less than 57

−∞<y<257
negative infinity less-than y less-than 257

57≤y≤257
57 less-than-or-equal-to y less-than-or-equal-to 257

A function can be modeled by the equation g(x)=6x−14
. Which gives the domain of the function?(1 point)
Responses

−∞<x<∞
negative infinity less-than x less-than infinity

−∞<y<∞
negative infinity less than y less than infinity

−∞<x<0
negative infinity less than x less than 0

−3≤x≤3

Dorian earns $15 every time he walks a dog. He models the total amount of money he makes walking dogs with the equation f(w)=15w
. Which inequality shows the range of his earnings given the real-world constraints?(1 point)
Responses

0<f(w)<1,050
0 less than f left parenthesis w right parenthesis less than 1,050

0≤f(w)≤1,050
0 less-than-or-equal-to f left parenthesis w right parenthesis less-than-or-equal-to 1,050

−∞<f(w)≤1,050
negative infinity less than f left parenthesis w right parenthesis less-than-or-equal-to 1,050

0≤f(w)<∞

Use the table to answer the question.

x y
2 3
3 5
4 7
5 9
6 11The table shows different values for a linear function. Calculate the rate of change of the function between 5 and 6.(1 point)
Responses

11
11

−2
negative 2

2
2

1/2

What is the rate of change of the function represented by the equation y=−3/5x+10
?(1 point)
Responses

10
10

3/5
Start Fraction 3 over 5 End Fraction

−3
negative 3

−3/5

Answer 1

Let's answer each question one by one.

1. Range of the function modeled by f(x) = 40x + 57:

   • The function represents the number of stamps in his collection after x weeks. Since x can be from 0 to 5 (inclusive), we find:
     • At x = 0: f(0) = 40(0) + 57 = 57
     • At x = 5: f(5) = 40(5) + 57 = 200 + 57 = 257
   • Thus, the stamps range from 57 (at week 0) to 257 (at week 5). Therefore, the correct representation of the range using inequality symbols is:
     • 57 ≤ y ≤ 257

2. Domain of the function modeled by g(x) = 6x - 14:

   • This is a linear function, which is defined for all real numbers. Therefore, the domain is:
     • −∞ < x < ∞

3. Range of Dorian's earnings modeled by f(w) = 15w:

   • Dorian earns money based on the number of dogs walked. Assuming there is a maximum limit of 70 dogs walked (since 15 * 70 = 1,050), his earnings would be:
     • The minimum he can earn is $0 (if he walks 0 dogs).
     • The maximum is $1,050 (if he walks 70 dogs).
   • Therefore, the correct representation of the range is:
     • 0 ≤ f(w) ≤ 1,050

4. Rate of change of the function between 5 and 6:

   • To find the rate of change, we use the formula (change in y)/(change in x):
     • From the table, at x = 5, y = 9 and at x = 6, y = 11.
     • Rate of change = (11 - 9) / (6 - 5) = 2 / 1 = 2.
   • Hence, the correct response is:
     • 2

5. Rate of change of the function represented by y = -3/5x + 10:

   • In a linear equation of the form y = mx + b, m represents the rate of change. Here, the slope m is -3/5.
   • Therefore, the correct answer is:
     • −3/5

Putting this all together:

1. 57 ≤ y ≤ 257
2. −∞ < x < ∞
3. 0 ≤ f(w) ≤ 1,050
4. 2
5. −3/5