Functions Unit Test

Question

2 of 152 of 15 Items
Question
Determine if 7x2+y=5
is a linear or nonlinear function.(1 point)
Responses

The function 7x2+y=5
is a nonlinear function.
The function 7 x squared plus y equals 5 is a nonlinear function.

The graph of the function 7x2+y=5
is not a straight line.
The graph of the function 7 x squared plus y equals 5 is not a straight line.

There is not enough information to determine if 7x2+y=5
is a linear or nonlinear function.
There is not enough information to determine if 7 x squared plus y equals 5 is a linear or nonlinear function.

The function 7x2+y=5
is a linear function.

Answer 1

To determine if the equation \(7x^2 + y = 5\) is a linear or nonlinear function, we can analyze it based on the degree of the variable \(x\).

1. A linear function can be expressed in the form \(y = mx + b\) (where \(m\) and \(b\) are constants) or can be rearranged to that form. In a linear function, the highest power of the variable \(x\) is 1.

2. In the equation \(7x^2 + y = 5\), the term \(7x^2\) contains \(x\) raised to the second power, which means it is a quadratic term.

Since the highest power of \(x\) in this equation is 2, we conclude that it does not meet the criteria for a linear function.

Based on this analysis, the correct response would be:

The function \(7x^2 + y = 5\) is a nonlinear function.