Final answer:
To find two explicit functions by solving for y in terms of x, you manipulate the equation to isolate y, making it the dependent variable. Examples include linear equations, where you calculate slope using two points, and more complex equations, like quadratics or exponentials, which may require different methods.
Step-by-step explanation:
When you are asked to find two explicit functions by solving the equation for y in terms of x, you are performing a task in algebra that involves manipulating the equation to express y as a function of x. This means you want to isolate y on one side of the equation, making it the dependent variable, determined by the values of the independent variable x. As the provided information suggests, if you know the functional relationship between x and y, you can generate and plot data pairs (x,y) to study the behavior of the function.
To illustrate the process of finding explicit functions, consider a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept. Using the given points on the line (X₁, Y₁) and (X₂, Y₂), you can calculate the slope using the formula m = (Y₂ - Y₁)/(X₂ - X₁). Once you have m and you know a point on the line or the y-intercept, you can write the equation of the line.
However, if we have a more complex function, we use different methods depending on the form of the function. For example, for a quadratic function of the form y = ax² + bx + c, you will likely need to complete the square or use the quadratic formula to solve for y if the function is equated to 0. For exponential functions, you might need log properties to solve for y in terms of x.