What information do you need to sketch a curve?

The following steps are taken in the process of curve sketching:

  1. Domain. Find the domain of the function and determine the points of discontinuity (if any).
  2. Intercepts.
  3. Symmetry.
  4. Asymptotes.
  5. Intervals of Increase and Decrease.
  6. Local Maximum and Minimum.
  7. Concavity/Convexity and Points of Inflection.
  8. Graph of the Function.

What is the algorithm for curve sketching?

An Algorithm for Sketching the Graph of y = f(x) Determine any discontinuities or limitations in the domain of f(x). For discontinuities, investigate the function’s values on either side of the discontinuity.

How do you find the symmetry of a curve sketch?

Symmetry about y axis The curve of an even function is symmetry about the y axis. This concept can be better understand by finding the symmetry of function f(x) = x2. Since f(-x) = -f(x), function f(x) = x2 is an even function and is symmetry about the y axis. This conclusion is confirmed by its graphic on the left.

WHY IS curve sketching important?

Curve sketching shows us how we can understand and predict the behavior of the function based on its first and second derivatives. Functions and their graphs are important not only in math but in other fields and applications as well.

How do you draw a graph step by step?

  1. Step 1: Identify the variables.
  2. Step 2: Determine the variable range.
  3. Step 3: Determine the scale of the graph.
  4. Step 4: Number and label each axis and title the graph.
  5. Step 5: Determine the data points and plot on the graph.
  6. Step 6: Draw the graph.

What are the steps involved in drawing a graph between two quantities?

Answer

  1. Check the two quantities for which graph has to be drawn.
  2. Draw a table and find corresponding values for both the quantities.
  3. Make sure to mark the quantities along with units on the graph by choosing a suitable scale.
  4. Plot the points on the graph using the table drawn and join the points to get the curve.

What is the slope of a curve?

The slope of a curve at a point is equal to the slope of the straight line that is tangent to the curve at that point.