Emma is an artist and has created seven paintings. she plans to paint three additional paintings each week. what statements are true of this scenario? check all that apply. the independent variable is represented by the output values. the dependent variable is the total number of paintings. the total number of paintings depends on the number of weeks that have passed. this scenario is a function because for each week that passes, there will be exactly one total number of paintings. the number of weeks is the output value.

The correct answers are:

The dependent variable is the total number of paintings; The total number of paintings depends on the number of weeks that have passed; and This scenario is a function because for each week that passes, there will be exactly one total number of paintings.

Explanation:

The two variables involved in this situation are the total number of paintings and the number of weeks that have passed.

The number of paintings changes because of the number of weeks that have passed, so the number of paintings is the dependent variable, or output value. This means the number of weeks is the independent variable, or input value.

Since there is only one output, number of paintings, for each input, number of weeks, this is a function.

It is required to judge the properties of the function. The correct statements are:

Given information:

Already created painting by Emma is 7.

She creates 3 paintings each week after creating the first 7.

Let the number of weeks be x and the total painting made after x week be y.

The given condition can be mathematically written as,

Here, x is an independent variable (input) which is the number of weeks. y is a dependent variable (output) which is the total number of paintings made.

The given condition predicts a function as there is only one value of y for each value of x. It is a linear function.

So, the correct statements are:

Therefore, statements 2, 3, and 4 are correct.

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