# Week 13 in Math 10

We started to learn Relations and Functions Unit this week. It might be the most difficult unit for me in math 10.

I learned about an independent variable and a dependent variable firstly. An independent variable is usually called x, and a dependent variable is usually called y or f(x). A dependent variable is changed by an independent variable in a functional formula. We can get x and y-incepts, a domain, and a range using those variables. When we should get a value of the x-intercept, we must substitute 0 for the y (x-intercept, 0), in contrast, how to get a value of the y-intercept is similarly substitute 0 for the x (0, y-intercept). A domain is the set of all of numbers for the independent variable (input x) in the relation, and a range is almost same as a domain excepting to change the independent variable to the dependent variable (output y). A relation is a comparison between two sets of elements and has connections more than one. A function is same as f(x) and has only one connection.

For example,

1. The cost of jellies is related to the weight

• The cost is a dependent variable, to output, a range, and y.
• The weight is an independent variable, to input, a domain, and x.
• It is a function.

2.

• It is a functionf(x) is same a function, and 2/3 x2 – 6 is a notation.
• x-intercept is to substitute 0 for y, 0 = 2/3 x2 – 6. So, the x-intercept is equal to 3 and -3.
• y-intercept is to substitute 0 for x, y = 2/3 * 02 -6. So, the y-intercept is equal to -6.
• A domain is the set of all of numbers for the independent variable in the relation. So, the domain is {-3 ≤ x ≤ 3, x ∈ R}
• A range is the set of all of numbers for the dependent variable in the relation. So, the range is {-6 ≤ y ≤ 3, y ∈ R}