Graphs of Functions

Consider a line that represents a linear function. Any point on the line has an x-coordinate for its horizontal position and a y-coordinate for its vertical position.

The horizontal coordinate x of a point is the independent variable. Substituting it into the function gives the vertical coordinate y, the dependent variable.

Multiple values of y are calculated by using different x-values in the function to plot the line.

The plot's domain includes all possible input values the function can accept, and the range consists of the corresponding output values it produces.

Nonlinear functions, such as even power functions, form U-shaped curves about their own vertical axis of symmetry.

These graphs often have non-negative y-values for both positive and negative x-values, and their outputs increase rapidly as the input moves away from zero.

Odd power functions often create S-shaped curves that extend in opposite directions, but their exact shape and position depend on the function’s form.

Similarly, reciprocal functions form two curves that approach the axes without touching them.

These axes act as asymptotes—lines the graph approaches indefinitely but never intersects.