Properties of Functions Quick Check

Question

2 of 52 of 5 Items

Question
Compare Linear Function 1 with Linear Function 2. Which one has the lesser initial value?

Linear Function 1: Lionel’s cell phone plan costs $45 per month.
Linear Function 2: The relationship between the number of months Ruby has had her cell phone (x)
and the total cost (y)
is given by y=40x+60
.
(1 point)
Responses

Linear Function 2 has the lesser initial value, with an initial value equal to $40 while Linear Function 1 has an initial value equal to $45.
Linear Function 2 has the lesser initial value, with an initial value equal to $40 while Linear Function 1 has an initial value equal to $45.

Linear Function 1 has the lesser initial value, with an initial value equal to $0 while Linear Function 2 has an initial value equal to $60.
Linear Function 1 has the lesser initial value, with an initial value equal to $0 while Linear Function 2 has an initial value equal to $60.

Linear Function 1 has the lesser initial value, with an initial value equal to $45 while Linear Function 2 has an initial value equal to $60.
Linear Function 1 has the lesser initial value, with an initial value equal to $45 while Linear Function 2 has an initial value equal to $60.

Linear Function 1 has the lesser initial value, with an initial value equal to $0 while Linear Function 2 has an initial value equal to $40.

Answer 1

To compare the initial values of both linear functions, we need to identify what those initial values are.

Linear Function 1:

• Lionel’s cell phone plan costs $45 per month.
  • This implies that the cost starts at $45 when \( x = 0 \), which means the initial value is $45.

Linear Function 2:

• The relationship is given by the equation \( y = 40x + 60 \).
  • Here, when \( x = 0 \), \( y = 40(0) + 60 = 60 \). This means the initial value is $60.

Now we can compare the initial values:

• Linear Function 1 has an initial value of $45.
• Linear Function 2 has an initial value of $60.

Since \( 45 < 60 \), we conclude that:

Linear Function 1 has the lesser initial value, with an initial value equal to $45 while Linear Function 2 has an initial value equal to $60.

So, the correct response is: Linear Function 1 has the lesser initial value, with an initial value equal to $45 while Linear Function 2 has an initial value equal to $60.