x2 y? f(z, y) = - 4 9 On the canvas below draw the level curves of f when z = - 9, z = – 4, z = 1, and z = : 4
Percentage
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Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
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Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
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Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
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![### Transcription and Explanation
#### Mathematical Expression
The function given is:
\[ f(x, y) = \frac{x^2}{4} - \frac{y^2}{9} \]
#### Instructions
You are asked to draw the level curves of \( f \) on the provided canvas for the following values of \( z \):
- \( z = -9 \)
- \( z = -4 \)
- \( z = 1 \)
- \( z = 4 \)
#### Grid Description
The graph is a 2D coordinate plane with:
- Horizontal axis (x-axis) and vertical axis (y-axis).
- Both axes range from -20 to 20 with grid lines spaced at intervals of 10 units.
#### Task
To plot the level curves, substitute each given value of \( z \) into the equation \( f(x, y) = z \) and solve for \( (x, y) \) to draw the curves corresponding to each \( z \) value on the coordinate plane.
#### User Interaction
Use the "Draw" tool to sketch the level curves on the canvas. The "Clear All" button is available to erase any drawings and start fresh.
These level curves represent the contours of the function \( f \) at different heights \( z \), showing how the function behaves over the plane.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F06a737e7-f57c-449b-94dc-ce666780f911%2F247d1226-33c7-4b86-b92c-50fff4122673%2F9ri7z_processed.png&w=3840&q=75)
Level Curves:
The level curves of a function f of two variables are the curves with equations , where z is a constant.
A level curve is the set of all points in the domain of f at which f takes on a given value z. In other words, it shows the graph of f where its height is z.
The given function is .
The level curves of the given function are of the form .
The given values of z are .
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