Does the table below represent a linear or nonlinear function?
A table titled 'Converting Inches to Centimeters' is shown. The first column, 'Inches' contains the values 1 through 4 in order top to bottom. The second column 'Centimeters' has the values 2.54, 5.08, 7.62, and 10.16 listed top to bottom.
(1 point)
Responses
nonlinear function
nonlinear function
linear function
linear function
The given table represents a linear function. Each value in the "Inches" column is multiplied by 2.54 to obtain the corresponding value in the "Centimeters" column. This consistent multiplication indicates a linear relationship between the two variables.
The ordered pairs (1, 1), (2, 8), (3, 27), (4, 64), and (5, 125) represent a function. What is a rule that represents this function?
(1 point)
Responses
y = x
y = x
y = 4x
y = 4x
y = x2
y = x 2
y = x3
To determine if the table represents a linear or nonlinear function, we need to check if there is a consistent pattern or relationship between the values in the "Inches" column and the corresponding values in the "Centimeters" column.
In this table, the relationship between inches and centimeters is consistent. Every inch is being multiplied by 2.54 to obtain the corresponding value in centimeters. Since the relationship can be described by a constant multiplier, this table represents a linear function.
Therefore, the correct answer is "linear function."