Final answer:
Parent functions include linear, quadratic, inverse (like cube root or logarithmic), and exponential. Linear functions are represented by straight lines, quadratic by parabolas, cube roots by 'S'-shaped curves, logarithmic functions by curves approaching the x-axis, and exponential by J-shaped curves.
Step-by-step explanation:
Identifying parent functions is an essential skill in understanding different types of equations and their graphs. Based on the information provided, certain parent functions are being discussed such as linear, quadratic, inverse (which could be logarithmic or cube root depending on context), and exponential functions.
A linear function is represented by the simple equation y = mx + b, where m is the slope and b is the y-intercept. The graph of a linear function is a straight line.
The quadratic function typically takes the form y = ax² + bx + c and its graph is a parabola. The inverse function could refer to a variety of functions including the inverse square (1/x²), the cube root function (y = ∛x), or the logarithmic function (y = log x). The cube root function graph typically resembles the letter 'S' stretched along the diagonal, whereas the logarithmic function graph is a curve that approaches but never touches the x-axis and rises rapidly after crossing the y-axis.
Finally, the exponential function has the form y = a·bx, where a is a constant, b is the base of the exponential, and the graph is an upward or downward sloping curve depending on the value of b.