How would you graph #y = ln(x^2) # without a calculator?

Answer 1

I tried with a....simplification...!

I would try using the base of the natural log (which is the irrational number #e=2.71828#) as being #3#. This is a huge simplification but it helps to make things easier for us.

So basically I would graph:

#y=log_3(x^2)#

Where the "real" graph is:

graph{ln(x^2) [-10, 10, -5, 5]}

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To graph ( y = \ln(x^2) ) without a calculator:

  1. Understand the function: ( \ln(x^2) ) means taking the natural logarithm of the square of ( x ).
  2. Identify key points:
    • Since ( \ln(x^2) ) is undefined for ( x \leq 0 ), we will focus on ( x > 0 ).
    • When ( x = 1 ), ( \ln(1^2) = \ln(1) = 0 ).
    • As ( x ) increases, ( \ln(x^2) ) also increases, but it increases at a decreasing rate due to the logarithmic nature.
    • The function is symmetrical around the y-axis.
  3. Plot key points:
    • Plot the point (1, 0) since ( \ln(1^2) = 0 ).
    • Plot other points symmetrically around the y-axis.
  4. Draw the curve:
    • Connect the plotted points smoothly, noting the asymptotic behavior as ( x ) approaches 0 from the right. The curve should approach negative infinity.
    • Label the axes and any key points if necessary.
  5. Verify the graph:
    • Ensure the graph reflects the properties of the function, such as being continuous and never crossing the x-axis.

By following these steps, you can graph ( y = \ln(x^2) ) without using a calculator.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7