Function Parameters

Grade 9 · algebra · 100 practice problems · read aloud

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Function Parameters: Understanding Input and Output

🎯 What Are Function Parameters?

Function parameters are the inputs or variables that you plug into a function rule. Think of a function as a machine: you put something in (the parameter), the machine does its work, and something new comes out.

Why it's useful: Parameters let us use the same function rule for many different input values. This is the foundation for modeling real-world situations, like calculating the total cost for any number of items.

📝 How to Evaluate Functions with Parameters

When you see f(x) = 2x + 3, x is the parameter. To evaluate the function, replace x with a given number and follow the order of operations.

  1. Identify the function rule and the parameter.
  2. Substitute the given number for the parameter.
  3. Simplify the expression using PEMDAS.

🔢 Worked Examples

Example 1: If f(x) = x² - 4, find f(3).

  1. Substitute: f(3) = (3)² - 4
  2. Simplify: = 9 - 4
  3. Answer: f(3) = 5

Example 2: If g(a) = 2a + 7, find g(-1).

  1. Substitute: g(-1) = 2(-1) + 7
  2. Simplify: = -2 + 7
  3. Answer: g(-1) = 5

⚠️ Common Mistakes to Avoid

Forgetting Parentheses: When substituting a negative number, always use parentheses! f(-2) becomes (-2), not -2. This prevents sign errors.

Misapplying Exponents: Remember that -3² = -9, but (-3)² = 9. The parentheses make a huge difference!

Confusing Notation: f(x) does not mean "f times x." It is read as "f of x" and means the function f evaluated at x.

💡 Tips & Tricks

Think "Input" and "Output": Create a simple T-chart to organize your work. List inputs (x) on one side and their corresponding outputs (f(x)) on the other.

Order of Operations is Key: Always follow PEMDAS after you substitute. Exponents and multiplication come before addition and subtraction.

Check Your Work: If you found f(0) = 3 for f(x)=2x+3, plug 0 back in to verify: 2(0)+3 does indeed equal 3.

🏀 How to Practice

  • Drill the Basics: Start by evaluating simple linear functions like f(x)=5x-2 for various values (e.g., f(1), f(10), f(-2)).
  • Mix It Up: Practice with functions that include exponents, like h(t) = t² + 1, to solidify the order of operations.
  • Create Your Own: Make up a function and a set of inputs. Evaluate them, then have a friend check your work!

Practice problems

6 of the 100, worked through step by step — try them before opening the answer.

1 2^(x+1) = 32

Hint: Express both sides with the same base, then set the exponents equal to each other.

Show the answer

Answer: 4

  1. Write down the given equation. 2^(x+1) = 32
  2. Recognize that both sides of the equation can be written as powers of 2. We know that 32 is the same as 2^5 because 2 * 2 * 2 * 2 * 2 = 32. So we rewrite the equation as: 2^(x+1) = 2^5
  3. Since the bases are the same (both are base 2), we can set the exponents equal to each other. This gives us the new equation: x + 1 = 5
  4. Solve for x by subtracting 1 from both sides of the equation. x + 1 - 1 = 5 - 1 x = 4
  5. State the final answer. The solution is x = 4.

2 log₂(32) = ?

Hint: Consider what power you need to raise the base to in order to get the argument. For example, log₃(27) asks: 3 to what power equals 27?

Show the answer

Answer: 5

  1. Recall that log₂(32) means "2 raised to what power equals 32?" So we write: 2^x = 32
  2. Express 32 as a power of 2. We know 32 = 2 × 2 × 2 × 2 × 2 = 2^5.
  3. Substitute 32 with 2^5 in the equation. So: 2^x = 2^5
  4. Since the bases are the same (base 2), we can equate the exponents. Therefore: x = 5
  5. This means log₂(32) = 5. Final answer: 5

We are asked to compute: log₂(32) = ?

3 log₂(64) = ?

Hint: Consider what power you need to raise 2 to in order to get the number inside the logarithm.

Show the answer

Answer: 6

  1. We are solving log₂(64) = ?
  2. This means we need to find the exponent x such that 2^x = 64.
  3. Write 64 as a power of 2: 64 = 2 × 2 × 2 × 2 × 2 × 2 = 2^6.
  4. Therefore, 2^x = 2^6, so x = 6.
  5. The answer is 6.

4 2^(x+1) = 32 = ?

Hint: Express both sides with the same base to solve for the variable in the exponent.

Show the answer

Answer: 4

  1. Recognize that 32 is a power of 2. 32 = 2 × 2 × 2 × 2 × 2 = 2^5.
  2. Rewrite the equation using this fact. 2^(x+1) = 2^5.
  3. Since the bases are the same (base 2) and are positive and not equal to 1, we can set the exponents equal to each other. x + 1 = 5.
  4. Solve for x. x = 5 - 1. x = 4.
  5. Check the answer. If x = 4, then 2^(4+1) = 2^5 = 32, which matches the given equation. Final answer: x = 4.

We are given: 2^(x+1) = 32.

5 log₃(27) + log₂(16) = ?

Hint: Remember that logarithms are the inverse of exponentiation. For example, log₄(64) asks '4 to what power equals 64?'

Show the answer

Answer: 7

  1. Evaluate log₃(27). This asks '3 to what power equals 27?' Since 3³ = 27, log₃(27) = 3.
  2. Evaluate log₂(16). This asks '2 to what power equals 16?' Since 2⁴ = 16, log₂(16) = 4.
  3. Add the results: 3 + 4 = 7.

The answer is 7.

6 y = 42(1.08)^x models Hana's investment. What does 42 represent? What does 1.08 represent?

Hint: In exponential functions of the form y = ab^x, the parameters have specific meanings related to starting values and growth patterns. Consider what each number tells you about the investment over time.

Show the answer

Answer: 42 represents the initial investment amount, 1.08 represents the growth factor per period

  1. Identify the function type: y = 42(1.08)^x is an exponential function in the form y = ab^x
  2. Interpret parameter a = 42: This is the initial value when x = 0. When x = 0, y = 42(1.08)^0 = 42(1) = 42. So 42 represents the starting investment amount.
  3. Interpret parameter b = 1.08: This is the growth factor. Since 1.08 = 1 + 0.08, this means the investment grows by 8% each period. The 1 represents 100% of the current value, and the 0.08 represents the 8% growth.
  4. Final interpretation: 42 represents the initial investment amount, and 1.08 represents the growth factor per period (8% growth).
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