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Substitution in functions is a foundational step in understanding how to evaluate a function with a specific value. It involves replacing the variable in the function's equation with a given number. In our exercise, we have the function \( y = \frac{1}{x^{2}} \). We know that we need to evaluate this function at a specific point, \( x = 2 \).

To substitute, simply replace \( x \) in the equation with \( 2 \). So, our function becomes \( y = \frac{1}{2^{2}} \). This substitution allows us to transform the function into a numerical expression that we can solve. The idea is to simplify the expression step-by-step, substituting efficiently to find an accurate result. It helps in understanding the behavior of functions when variables change.

Expression evaluation refers to calculating the value of an algebraic expression after substituting the variables with given numbers. After substituting in the function \( y = \frac{1}{x^{2}} \) with \( x = 2 \), we get \( y = \frac{1}{2^{2}} \).

Let's evaluate this expression:

• First, calculate the exponent: \( 2^{2} = 4 \).
• Then, compute the fraction: \( \frac{1}{4} = 0.25 \).

Thus, the value of \( y \) when \( x = 2 \) is \( 0.25 \).
This step is crucial because it allows us to see how the function behaves numerically. Understanding this helps when predicting outcomes in more complex mathematical problems. By performing each step methodically, it ensures accuracy and builds a solid foundation for more complex evaluations.

Table completion involves filling out values in a table based on an evaluated function. It is an essential skill when organizing data efficiently. In the exercise, we've evaluated the function for a specific \( x \) value and found \( y \).

In this scenario:

• When \( x = 2 \), the value of \( y \) is \( \frac{1}{4} \).

With this information, we can fill out the corresponding column in the table with these values.
Completing tables is fundamental to visualizing relationships between variables. They provide clarity by showing how changes in one variable affect another. This process ensures that data is organized, making it easier to interpret and analyze further. It's an essential skill not only in mathematics but also in data management and science as a whole.