The equation y−3=4(x+1) represents a linear equation (a straight line) in slope intercept form: y=4x+7

For a straight line, there are no restrictions on x. Therefore, the domain is all real numbers:

Domain: (-infinite, infinite)

Similarly, since a line extends infinitely in both directions for y, the range is also all real numbers:

Explain what the domain and range mean by your own words.

• Domain: The domain of the graph is all the possible values of x, that means that any real number can be used as an input for the equation. There are no restrictions on x.
• Range: The range of the graph is all the possible values of y, meaning the output or y value can also be any real number. There are no restrictions on y since the line extends infinitely in both directions.

Is my graph a function or not?

Yes the graph is a function, this can be confirmed using the Vertical Line Test, any vertical line drawn on the graph will intersect the line at exactly one point.

This means each input x value corresponds to exactly one output y value, which satisfies the definition of a function.

1. Give an example from this assignment where you represented the same mathematical idea in multiple ways?

An example of representing the same mathematical idea in multiple ways is: The equation was given in point slope form: y−3=4(x+1). It was rewritten in slope-intercept form: y=4x+7

2. Give an example from this assignment where you used mathematical vocabulary to demonstrate your understanding.

I used mathematical vocabulary like domain (all possible x values), range (all possible y values), and the Vertical Line Test (to confirm the graph is a function) to demonstrate my understanding.

3. Give an example from this assignment where you used formatting to share the information in a clear and organized way.

I used formatting by breaking the problem into sections (like Domain, Range, and Function Test) (y=4x+7) and (−infinite, infinite) to make the information easy to follow.