91Ó°ÊÓ

Evaluating functions involves finding the output of a function for a given input. A function can be thought of like a machine where you put in a value (input), and the function processes it to give a new value (output). In our exercise, we have the function: \( f(x) = 7.5x + 15 \) To evaluate this function at a specific point, we substitute our input value into the function. For instance, to find \( f(-2) \), substitute -2 for every \( x \) in the equation: \( f(-2) = 7.5(-2) + 15 \).Evaluating functions using this method allows us to understand the behavior of the function at different points. It's a fundamental skill in algebra and helps to solve real-world problems by understanding mathematical relationships.

The substitution method is used in algebra to replace a variable with a given value. This method simplifies the expressions and allows us to solve for unknowns. In our example, we use the substitution method to evaluate the function \( f(x) = 7.5x + 15 \) at \( x = -2 \).Here’s how we do it step-by-step:

• Take the given function: \( f(x) = 7.5x + 15 \).
• Substitute \( -2 \) into the function where \( x \) is: \( f(-2) = 7.5(-2) + 15 \).
• Now, perform the operations as indicated: first, the multiplication, and then the addition.

Substitution simplifies complex algebraic expressions and is a crucial technique in solving equations and working with functions.

An algebraic expression is a combination of numbers, variables, and arithmetic operations like addition, subtraction, multiplication, and division. In our problem, the algebraic expression is: \( 7.5x + 15 \).Breaking it down, we have:

• The coefficient 7.5, which multiplies the variable \( x \).
• The constant term 15, which is added to the product of the coefficient and variable.

To solve the given problem, we perform operations on the algebraic expression by following the rules of arithmetic. When evaluating the function for a specific value, always replace the variable with the given number and calculate accordingly:

For our example, we substitute \( -2 \), and simplify:

• \( 7.5(-2) = -15 \),
• Then add the constant: \( -15 + 15 = 0 \).

Simplifying algebraic expressions helps us solve equations more efficiently and understand the relationships between variables and constants.