Question

What are the important aspects to look for in a graph in order to accurately identify the function family the graph is from?

a) The presence of asymptotes
b) The shape of the curve
c) The number of critical points
d) The x-intercepts and y-intercepts

Answer 1

To accurately identify the function family of a graph, important aspects to look for include the presence of asymptotes, the shape of the curve, the number of critical points, and the x-intercepts and y-intercepts.

Step-by-step explanation:

The important aspects to look for in a graph in order to accurately identify the function family are:

1. The presence of asymptotes: Different function families have different types of asymptotes. For example, a rational function may have vertical asymptotes, while an exponential function may have horizontal asymptotes.
2. The shape of the curve: Each function family has a distinct shape. For example, a parabola represents a quadratic function, while a straight line represents a linear function.
3. The number of critical points: Critical points occur where the derivative of the function is zero or undefined. Different function families have different numbers of critical points. For example, a cubic function may have two critical points.
4. The x-intercepts and y-intercepts: The x-intercepts and y-intercept of a graph can provide important information about the function family. For example, a linear function will have a single x-intercept and y-intercept.