Additional Graphing Exercises

[Technology Exercise] Graph the curves in Exercises 109–112. Explain the relationship between the curve’s formula and what you see.

y = −1 / √(4 − x²)

Guida verificata passo dopo passo

Step 1: Understand the function y = −1 / √(4 − x²). This is a rational function where the numerator is a constant (-1) and the denominator is a square root function. The expression inside the square root, 4 - x², is a quadratic expression.

Step 2: Identify the domain of the function. The expression inside the square root, 4 - x², must be greater than zero for the function to be defined. Solve the inequality 4 - x² > 0 to find the domain.

Step 3: Determine the behavior of the function as x approaches the boundaries of the domain. Consider the limits as x approaches the values where 4 - x² equals zero, which are the points where the function is undefined.

Step 4: Analyze the symmetry of the function. Since the expression inside the square root is even (4 - x²), the function is symmetric with respect to the y-axis. This means the graph will be mirrored on either side of the y-axis.

Step 5: Use technology to graph the function. Input the function into graphing software or a graphing calculator to visualize the curve. Observe how the graph behaves near the boundaries of the domain and note any asymptotic behavior.

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