Linear Function

Q.

Write a function rule for “the output is eleven more than the input.”

Q. A milk vendor mixes water with pure milk in the ratio of $1:3$ while processing it. The vendor dispatches $50\text{L}$ of the mixed milk each day. Determine the total quantity of mixed milk in terms of quantity of pure milk used. Is this a function?

1. Yes, this is a non-linear function.
2. This is not a linear function as three variables are involved.
3. Total quantity of mixed milk is four-third of the quantity of pure milk.
4. Total quantity of mixed milk is two-third of the quantity of pure milk.

Q. $y=2x+2$ is a

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

Q.

When is it appropriate to model data with a linear function Given a example of world data that can be modeled with a linear function include the linear function and a sample of the data.

Q. For the equation $y=f\left(x\right)$, a function is said to be a linear function if the exponents on the $x$'s are either 0 or

1. 1

Q. Determine whether the data from the following table represents a linear function:

1. Yes
2. No

Q. Consider the following statements:

Statement I: Any graph that passes the vertical line test is a linear function.

Statement II: All straight lines are linear functions.

1. Both statements are correct.
2. Only one statement is correct.
3. Both statements are wrong.

Q.

Write in the exponential form.

$axaxaxaxaxaxa=a^7$

Q. What will be the value of $y$ for the point a?

Q. Identify which is/are not a linear function.

1. 
2. 
3. 
4. 

Q. In a grocery shop, the bill of Adam is $y=1000x+4000$. The bill given to him is a

1. Function not a relation
2. Non linear function
3. Linear- function
4. Constant function

Q. Initial height of a plant is $50\text{cm}.$ Each day its height increases by $0.5\text{cm}.$ Can the total height of the plant be represented as a linear function of number of days? If yes, obtain the function.

1. No. It will not result a linear function.
2. Yes. The function is $h=\frac{1}{2}d,$ where, $h$ is the height in $cm,$ and $d$ is the number of days.
3. Yes. The equation is $h=50+\frac{1}{2}d,$ where, $h$ is the height in $cm,$ and $d$ is the number of days.
4. It is a relation but not a function.

Q. Choose the following with their correct options

1. $y=x$
2. Linear function
3. $y=1$
4. Same output
5. $x=6$
6. Relation only
7. $y=x^3$
8. Cubic function

Q.

Express the following algebraic expressions in exponential form.

$2\times 5\times x\times x\times y$

Q. Find the output $y$, when input, $x$, is $-35$.

$y=50-\frac{x}{7}+2$

Q. Identify the linear function(s).

1. $\frac{x}{y}=\sqrt{5}$
2. $\frac{1}{x}=\frac{1}{y}$
3. $x=y^0$
4. $y=x^{\frac{5}{3}-\frac{2}{3}}+\frac{1}{3}$

Q. What will be the linear function of the following?

1. $y=2x+x$
2. $y=2x+1$

Q. What would be the value of '$y$' when '$x=-5$' for the equation of line $y=3x$?

1. 15
2. -15
3. 9
4. -9