Question

Write a rule in function notation for each situation:


1. Sales tax is 7% of the total price

2. For f(x) = 1/4x + 10, find x such that f(x) = 14


Then,

3. Identify the independent and dependent variables.


"The essay instructions were to write three facts about each person listed."

Answer 1

Answer:

1. $\bold{S=f(P) = 0.07P}$

2. x = 16

3. Part 1: P is the independent variable and S is the dependent variable.

Part 2: x is the independent variable and y is the dependent variable.

Step-by-step explanation:

1. To write the function notation for:

Sales tax is 7% of the total price.

Let the total price be $P$.

And sales tax be $S$.

As per the given statement:

$S = 7\% \ of\ P\\\Rightarrow S =\dfrac{7}{100}P\\\Rightarrow S=0.07P$

Writing it in the function notation:

$\bold{S=f(P) = 0.07P}$

2. To find the value of x such that $f(x) = 14$ and

$f(x) = \dfrac{1}4x + 10$

Putting the value of $f(x) = 14$

$14 = \dfrac{1}4x + 10\\\Rightarrow \dfrac{1}4x =14-10\\\Rightarrow \dfrac{1}4x =4\\\Rightarrow x =4\times 4\\\Rightarrow \bold{x =16}$

3. To find the dependent and independent variable.

Independent variables are those whose value is not dependent on the other variable's values.

Dependent variables are dependent on the value of other variables.

In question 1:

$\bold{S=f(P) = 0.07P}$

P is the independent variable.

S is the dependent variable.

In question 2:

If we write it as follows:

$y=f(x) = \dfrac{1}4x + 10$

x is the independent variable and y is the dependent variable.