Now substitute \(x = 3\) into the function to find the corresponding \(y\)-coordinate:

["Title: How to Substitute (x = 3) into a Function to Find the (y)-Coordinate — A Step-by-Step Guide", "When studying functions in algebra and calculus, one essential skill is substituting values into functions to determine their corresponding outputs. Understanding how to find the (y)-coordinate by substituting (x = 3) is a fundamental technique used in graphing, analysis, and problem-solving. In this article, we’ll walk through the process of evaluating a function at (x = 3) and extracting the corresponding (y)-value with clear examples and best practices.", "---", "### What Does It Mean to Substitute (x = 3) into a Function?", "Substituting (x = 3) means replacing every instance of the variable (x) in the function’s expression with the number 3. This substitution helps determine the exact output (y), also known as the function’s value, when the input is 3. It’s a basic yet powerful step in evaluating functions for graphs, equations, calculus, and real-world applications.", "---", "### Step-by-Step Example", "Let’s consider a sample function to illustrate:\n[ f(x) = 2x^2 + 5x - 7 ]", "To find the (y)-coordinate when (x = 3), substitute 3 for (x) in the equation:", "[\nf(3) = 2(3)^2 + 5(3) - 7\n]", "Now compute step-by-step:", "1. (3^2 = 9)\n2. (2 \cdot 9 = 18)\n3. (5 \cdot 3 = 15)\n4. Combine: (18 + 15 - 7 = 26)", "So, (f(3) = 26), meaning the corresponding point on the graph is ((3, 26)).", "---", "### Why Finding the (y)-Coordinate Matters", "Determining (y) from (x) substitution serves multiple purposes:", "- Graphing Functions: Marks key points on the coordinate plane.\n- Analyzing Trends: Helps identify function behavior and shape.\n- Solving Equations: Useful when looking for specific outputs or roots.\n- Applied Problems: Calculating values in physics, economics, or engineering models.", "---", "### Tips for Accurate Substitution", "- Double-check your sign: (x = 3) could represent (+3) or depend on context.\n- Handle exponents carefully—order of operations is crucial.\n- Use parentheses properly when combining multiple operations.\n- Verify each step to avoid arithmetic errors.", "---", "### Conclusion", "Substituting (x = 3) into a function is a simple yet critical operation that unlocks the function’s value at a specific input. By systematically replacing variables and computing step-by-step, anyone can accurately determine the corresponding (y)-coordinate. Whether you’re drafting graphs, solving equations, or modeling real data, mastering this skill forms a solid foundation for success in math and beyond.", "Key Takeaway:\nTo find the (y) value, substitute (x = 3) into the function’s expression and simplify algebraically. Practice with different functions to build confidence and precision.", "---", "Keywords for SEO:\nsubstitute (x = 3) into a function, find (y)-coordinate, evaluating a function at (x = 3), how to compute function output, step-by-step function evaluation, graph a function, algebra practice."]