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How to Put Log Fuciton Into Graph on Ti Calculator

Reviewed by Calculator Editorial Team

Graphing logarithmic functions on TI calculators is a valuable skill for students and professionals in mathematics, science, and engineering. This guide provides step-by-step instructions, practical examples, and a built-in graphing calculator to help you master this essential technique.

Basic Steps to Graph a Log Function

Before diving into TI calculator specifics, let's review the fundamental steps for graphing any logarithmic function:

  1. Identify the function: Determine the base of the logarithm and the expression inside (argument). Common forms include y = logₐ(x) and y = logₐ(bx + c) + d.
  2. Find key points: Calculate specific y-values for various x-values, especially at x = 1 (y = 0) and where the argument equals 1 (x = 0 for y = logₐ(x)).
  3. Determine asymptotes: Vertical asymptotes occur where the argument is zero (x = -c/b for y = logₐ(bx + c)).
  4. Identify intercepts: The x-intercept is where y = 0 (x = 1 for y = logₐ(x)).
  5. Plot the points: Use the calculated points to sketch the curve, remembering that logarithmic functions grow very slowly as x increases.

Key Properties of Logarithmic Functions:

  • Domain: x > 0 (for y = logₐ(x))
  • Range: All real numbers
  • Vertical asymptote: x = 0
  • x-intercept: (1, 0)
  • Behavior: Grows slowly as x increases

TI Calculator-Specific Instructions

TI graphing calculators provide powerful tools for visualizing logarithmic functions. Here's how to use them effectively:

Step 1: Set Up the Window

Proper window settings are crucial for clear graphs. For most logarithmic functions:

  • Xmin: -10
  • Xmax: 10
  • Xscl: 1
  • Ymin: -10
  • Ymax: 10
  • Yscl: 1

Step 2: Enter the Function

For the basic function y = log(x):

  1. Press Y= to access the equation editor
  2. Enter the function: log(X)
  3. Press GRAPH to view the result

Step 3: Adjust for Different Bases

TI calculators default to base 10 logarithms. For natural logarithms (base e):

  1. Enter ln(X) instead of log(X)
  2. For other bases, use the change of base formula: logₐ(x) = ln(x)/ln(a)

Pro Tip: When graphing transformed functions like y = log(2x + 3) - 4, carefully adjust your window settings to ensure the entire graph is visible. You may need to zoom in or out using the ZOOM and TRACE features.

Worked Examples

Example 1: Basic Logarithmic Function

Graph y = log(x) on a TI calculator:

  1. Set window as described above
  2. Enter log(X) in Y1
  3. Press GRAPH to see the curve starting at (1,0) and increasing slowly

Example 2: Transformed Function

Graph y = log(x - 2) + 3:

  1. Adjust window: Xmin = -5, Xmax = 15, Ymin = -5, Ymax = 15
  2. Enter log(X-2)+3 in Y1
  3. Note the vertical shift up 3 units and horizontal shift right 2 units

Common Transformations:

  • y = log(x) + c: Vertical shift up by c units
  • y = log(x - h): Horizontal shift right by h units
  • y = a*log(x) + c: Vertical stretch by a and shift up by c

Common Issues and Fixes

When graphing logarithmic functions on TI calculators, you may encounter these common problems:

1. Function Not Displaying

Possible causes and solutions:

  • Incorrect syntax: Use parentheses properly (e.g., log(2X) not log2X)
  • Window too narrow: Adjust Xmin/Xmax to include key points
  • Function undefined: Ensure argument is positive (x > 0 for y = log(x))

2. Graph Not Visible

Try these adjustments:

  • Zoom out using ZOOM → ZoomOut
  • Check Y= editor to ensure function is active
  • Verify window settings include the graph's range

3. Asymptote Not Clear

To make vertical asymptotes more visible:

  • Use a thicker line style for the asymptote
  • Adjust window to show the approach to infinity
  • Use TRACE to follow the curve near the asymptote

Frequently Asked Questions

Q: Can I graph logarithmic functions with different bases on my TI calculator?
A: Yes, you can use the change of base formula: logₐ(x) = ln(x)/ln(a). Simply enter this expression in the Y= editor.
Q: How do I graph inverse logarithmic functions on my TI calculator?
A: For inverse functions like y = 10ˣ, enter 10^X in the Y= editor. These exponential functions are inverses of logarithmic functions.
Q: What should I do if my graph looks like a straight line?
A: This typically indicates a linear function rather than a logarithmic one. Double-check your function entry and ensure you're using the log() function rather than a linear expression.
Q: How can I save my logarithmic graph for later use?
A: Use the PRGM → SavePic feature to save the current graph as an image. You can also use the PRINT function to send the graph to a printer.