The type of mathematical function that does NOT have a defined shape when graphed is the logarithmic function.
Explanation:
1. Linear functions have a straight line shape when graphed. They follow the form y = mx + b, where m is the slope and b is the y-intercept.
2. Quadratic functions have a parabolic shape when graphed. They follow the form y = ax^2 + bx + c, where a determines the direction and width of the parabola.
3. Square root functions have a curved shape when graphed. They follow the form y = √x and represent the positive square root of x.
4. Logarithmic functions do not have a defined shape when graphed. They follow the form y = logₐ(x), where a is the base of the logarithm. The graph of a logarithmic function is characterized by an asymptotic behavior, which means it approaches but never touches a certain line called the asymptote.
In summary, among the given options, the logarithmic function is the one that does not have a specific shape when graphed, as its graph does not conform to a standard geometric shape like a line, parabola, or curve.
