Evaluate Function Game

Evaluate Function Game
This game will require you to find the correct output (f(x)) for every given input (x). Scroll down for a detailed explanation.
 

 

How to Play the Evaluate Function Game

1. Analyze the Equation:
   Look at the large white text in the center (e.g., f(x) = -2x + 5). This is your “instruction manual” for how to change the number.
   
2. Identify the Input:
   Look at the indigo box that says Target Input (e.g., x = 3). This is the number you are going to “plug into” the equation.
   
3. Perform the Calculation: Replace the x in the equation with your target number and solve using the order of operations.
   
4. Submit: Type your final answer in the box and click Submit Calculation (or hit Enter).
   Correct: You gain 10 points and a new problem appears.
   Incorrect: The lab shakes! Check your signs (positive/negative) and try again.
   

Solving the Different Machines
The lab uses three different types of functions. Here is how to handle them:

1. The Linear Machine (f(x) = ax + b)
   Action: Multiply the input by the coefficient (a), then add or subtract the constant (b).
   Example: f(x) = -3x + 4 where x = 2.
   -3 · (2) = -6
   -6 + 4 = -2
   Answer: -2
   

2. The Quadratic Machine (f(x) = ax² + b)
   Action: Square the input first, then multiply by the coefficient, then add the constant.
   Crucial Rule: Any number squared is positive.
   Example: f(x) = -x² + 10 where x = -3.
   (-3)² = 9
   Apply the negative: -9
   -9 + 10 = 1
   Answer: 1
   

3. The Absolute Value Machine (f(x) = a|x + b|)
   Action: Solve what is inside the bars first. If it’s negative, make it positive. Then multiply by the number outside.
   Example: f(x) = -2|x + 5| where x = -7.
   Inside: -7 + 5 = -2
   Absolute value: |-2| = 2
   Multiply by outside: -2 · (2) = -4
   Answer: -4
   

How to Evaluate Functions?

1. The Notation
   When you see f(x) = 2x + 3, it is read as “f of x equals 2x plus 3."
   f: The name of the function.
   x: The input (the placeholder).
   2x + 3: The rule or “recipe” to follow.
   

2. The Three-Step Process
   To evaluate a function like f(x) = x² - 4 for x = 5:
   Step 1: Substitution
   Replace every instance of the variable (x) with the given number. Always use evaluateheses during this step to avoid mistakes with negative numbers.
   f(5) = (5)² - 4
   Step 2: Order of Operations (PEMDAS)
   Follow the standard rules: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
   First, handle the exponent: 5² = 25.
   Now the equation looks like: 25 - 4.
   Step 3: Simplify
   Perform the final calculation to get your result.
   25 - 4 = 21
   Final Answer: f(5) = 21.
   This means when the input is 5, the output is 21.
   

3. Dealing with Negative Numbers
   Negative numbers are where most mistakes happen, especially with exponents.
   Example: Evaluate f(x) = -x² for x = -3.
   Substitute with evaluateheses: f(-3) = -(-3)²
   Evaluate the exponent first: (-3) · (-3) = 9.
   Apply the negative sign outside: -(9) = -9.
   Note: Without evaluateheses, you might mistakenly think -3² is the same as (-3)². They are not.
   

4. Evaluating from a Graph
   You don’t always need an equation. If you have a graph and you are asked to “Find f(2)”:
   Find 2 on the horizontal x-axis.
   Move your finger up or down until you hit the graph line.
   Look across to the vertical y-axis to see the value. That is your answer.
   

This video gives a clear, step-by-step approach to evaluate functions.

• Show Video

 

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