A sketch curve is a visual representation of a mathematical equation or function. It is created by plotting points on a coordinate plane according to the given equation, and then connecting these points to form a curve.
Parametric equations are a set of equations that express the coordinates of a point in terms of one or more parameters. These equations are used to describe the motion of a point or object in a two- or three-dimensional space.
The equations x=e^-t+t and y=e^t-t represent parametric equations for a curve. The variable t represents the parameter, and as t increases, the coordinates (x,y) of the point on the curve change accordingly.
To sketch the curve, you can plot points by substituting different values for t in the given equations. Then, connect these points to form a smooth curve. You can also use a graphing calculator or software to graph the curve.
The parameters in these equations represent the independent variable, t, which controls the motion of the point or object on the curve. By changing the values of t, you can explore different points on the curve and see how they are connected.