Example of Function Equation

Question

Linear Function
Quadratic Function
Absolute Value Function
Exponential Growth Function
Exponential Decay Function
Cube Root Function
Cubic Function
Square Root Function

Answer 1

Here are examples of each of the specified function types:

1. Linear Function: \[ f(x) = mx + b \] Example: \[ f(x) = 2x + 3 \]

2. Quadratic Function: \[ f(x) = ax^2 + bx + c \] Example: \[ f(x) = x^2 - 4x + 4 \]

3. Absolute Value Function: \[ f(x) = |x| \] Example: \[ f(x) = |2x - 5| \]

4. Exponential Growth Function: \[ f(x) = a \cdot b^x \quad \text{(where } b > 1\text{)} \] Example: \[ f(x) = 3 \cdot 2^x \]

5. Exponential Decay Function: \[ f(x) = a \cdot b^{-x} \quad \text{(or equivalently, } f(x) = a \cdot \frac{1}{b^x} \text{ where } b > 1\text{)} \] Example: \[ f(x) = 5 \cdot (0.5)^x \]

6. Cube Root Function: \[ f(x) = \sqrt[3]{x} \] Example: \[ f(x) = \sqrt[3]{x - 2} \]

7. Cubic Function: \[ f(x) = ax^3 + bx^2 + cx + d \] Example: \[ f(x) = 2x^3 - 3x^2 + x - 5 \]

8. Square Root Function: \[ f(x) = \sqrt{x} \] Example: \[ f(x) = \sqrt{x + 3} \]

Feel free to ask if you need any additional information or clarification on these functions!

Answer 2

what are the math examples

Answer 3

Sure! Here are mathematical examples for each of the mentioned functions, including specific cases for better understanding:

1. Linear Function:

   • Function: \( f(x) = 2x + 3 \)
   • Example Calculation:
     • For \( x = 1 \): \[ f(1) = 2(1) + 3 = 5 \]
     • For \( x = -1 \): \[ f(-1) = 2(-1) + 3 = 1 \]

2. Quadratic Function:

   • Function: \( f(x) = x^2 - 4x + 4 \)
   • Example Calculation:
     • For \( x = 2 \): \[ f(2) = 2^2 - 4(2) + 4 = 0 \]
     • For \( x = 3 \): \[ f(3) = 3^2 - 4(3) + 4 = -2 \]

3. Absolute Value Function:

   • Function: \( f(x) = |2x - 5| \)
   • Example Calculation:
     • For \( x = 3 \): \[ f(3) = |2(3) - 5| = |6 - 5| = 1 \]
     • For \( x = 2 \): \[ f(2) = |2(2) - 5| = |4 - 5| = 1 \]

4. Exponential Growth Function:

   • Function: \( f(x) = 3 \cdot 2^x \)
   • Example Calculation:
     • For \( x = 0 \): \[ f(0) = 3 \cdot 2^0 = 3 \cdot 1 = 3 \]
     • For \( x = 2 \): \[ f(2) = 3 \cdot 2^2 = 3 \cdot 4 = 12 \]

5. Exponential Decay Function:

   • Function: \( f(x) = 5 \cdot (0.5)^x \)
   • Example Calculation:
     • For \( x = 1 \): \[ f(1) = 5 \cdot (0.5)^1 = 5 \cdot 0.5 = 2.5 \]
     • For \( x = 3 \): \[ f(3) = 5 \cdot (0.5)^3 = 5 \cdot 0.125 = 0.625 \]

6. Cube Root Function:

   • Function: \( f(x) = \sqrt[3]{x} \)
   • Example Calculation:
     • For \( x = 8 \): \[ f(8) = \sqrt[3]{8} = 2 \]
     • For \( x = -27 \): \[ f(-27) = \sqrt[3]{-27} = -3 \]

7. Cubic Function:

   • Function: \( f(x) = 2x^3 - 3x^2 + x - 5 \)
   • Example Calculation:
     • For \( x = 1 \): \[ f(1) = 2(1)^3 - 3(1)^2 + (1) - 5 = 2 - 3 + 1 - 5 = -5 \]
     • For \( x = 2 \): \[ f(2) = 2(2)^3 - 3(2)^2 + (2) - 5 = 16 - 12 + 2 - 5 = 1 \]

8. Square Root Function:

   • Function: \( f(x) = \sqrt{x} \)
   • Example Calculation:
     • For \( x = 9 \): \[ f(9) = \sqrt{9} = 3 \]
     • For \( x = 4 \): \[ f(4) = \sqrt{4} = 2 \]

These examples illustrate how to compute values for each type of function using provided input values. If you have any further questions or need additional information, feel free to ask!