Non Linear Function

Q. A function whose graph is not a straight line is called a non-linear function.

1. True
2. False

Q. Consider the statements regarding non-linear functions.

Statement I: A function which are not straight lines are non-linear functions.

Statement II: Non-linear functions in form of $y=f\left(x\right)$ have atleast one term in which exponent of $x$ is other than $0$ or $1.$

1. Both the statements are correct.
2. Only one statement is correct.
3. None of the statements are correct.

Q. Every curve that is not a straight line is not necessarily a non-linear function.

1. True
2. False

Q. Consider the following statements:

Statement I: Every curve that is not a straight line is a non-linear function.

Statement II: A non-linear function must pass the vertical line test.

1. Both the statements are correct.
2. Only statement I is correct.
3. None of the statements are correct.

Q. If a curve passes the vertical line test and it is not a straight line, then it is

1. Linear function
2. Non-linear function
3. Not a function

Q. Identify the nonlinear function(s).

1. $y=x^e-e$
2. $y=x^{(2-\frac{1}{2})-1.5}-x^{\frac{(2-\frac{1}{2})}{1.5}}$
3. $f\left(t\right)=4t^3-2t^2-t$
4. $xy=1$

Q. Match the following

1. Non-linear function
2. Linear function
3. Non-linear function
4. Non-linear function

Q. Cost of a balloon is inversely proportional to number of balloons purchased. Comment on the relationship of the rate of reaction with time.

1. Cost of a balloon is a function of number of balloons purchased.
2. From the defination of a function, the relationship between the cost of balloon and number of balloons purchased is not a function.
3. The relationship is non-linear.
4. The relationship is linear as the exponent of the variables is $1.$

Q. A car racer is varying the speed of the car proportional to the square root of time. Is the speed of the car during the forward motion a non-linear function of time? Answer in Yes/No.