Question

A lawn-mowing company is trying to grow its business. It had 26 clients when they started its business and wants to increase by 3 new clients each week. Use an arithmetic sequence to write a function to represent this real-world situation and determine the range of the function for the first four weeks of data. A) f(x) = 3x + 26; 0 ≤ y ≤ 4 B) f(x) = 3x + 26; 26 ≤ y ≤ 35 C) f(x) = 3x + 23; 26 ≤ y ≤ 35 D) f(x) = 3x + 23; 0 ≤ y ≤ 4

Answer 1

f(x) = 3x + 26; 26 ≤ y ≤ 35

Explanation:

This makes a linear equation.

y=mx+b

where m is the amount they want to increase each week

and b is the initial value i.e 26 clients.

Now substitute the values in the equation.

Let x=0

y=3(0)+26

y = 26

Now let x= 3

y=mx+b

y=3(3)+26

y=9+26

y=35

Answer 2

f(x) = 3x + 26; 26 ≤ y ≤ 35

Explanation:

This makes a linear equation.

y=mx+b

where m is the amount they want to increase each week

and b is the initial value i.e 26 clients.

Now substitute the values in the equation.

Let x=0

y=3(0)+26

y = 26

Now let x= 3

y=mx+b

y=3(3)+26

y=9+26

y=35

Thus the correct option is B.

f(x) = 3x + 26; 26 ≤ y ≤ 35 .....