give examples of what it means to have a relation that shows y as a function of x
1. A simple linear equation: y = 3x + 2. In this relation, y is a function of x because for every value of x, there is a corresponding value of y that can be calculated using the equation.
2. The equation of a parabolic curve: y = x^2 - 4x + 3. In this relation, y is a function of x because for each value of x, there is only one corresponding value of y determined by the equation.
3. The exponential function: y = 2^x. In this relation, y is a function of x because the value of y is uniquely determined by the value of x in the exponential equation.
4. The trigonometric function: y = sin(x). In this relation, y is a function of x because the value of y (sine of x) is dependent on the angle x, making it a one-to-one mapping between x and y values.