Evaluating Functions

TL;DR

This content explains the concept of function definition using the equation g(x) = 8x + 2 and demonstrates how to find g(0), g(-5), and g(2x + 3) by substituting the values.

Transcript

Given g of x is equal to 8x plus 2, find g of zero, g of negative 5, and g 2x plus 3. So all this is, when they say g of x is equal to 8x plus 2, this is a function definition. They're saying you give me any x, and you input it into my function g, and my function g will output, will associate with that number x, another number that happens to be 8x... Read More

Key Insights

• 💨 Function definition is a way to create associations between input and output values.
• 👻 Substituting specific values into a function equation allows us to find corresponding output values.
• 🟰 g(0) is equal to 2, g(-5) is equal to -38, and g(2x + 3) simplifies to 16x + 26.
• 🪜 The equation g(x) = 8x + 2 follows the general pattern of multiplying the input value by 8 and adding 2 to calculate the output value.

Questions & Answers

Q: What does the equation g(x) = 8x + 2 represent?

The equation represents a function definition, where any input value of x is multiplied by 8 and then 2 is added to the result, giving the corresponding output value.

Q: How do you find g(0)?

To find g(0), substitute 0 into the equation as the input value of x, resulting in g(0) = 8(0) + 2 = 2.

Q: What is the value of g(-5)?

By substituting -5 into the equation as the input value of x, we get g(-5) = 8(-5) + 2 = -40 + 2 = -38.

Q: How do you find g(2x + 3)?

To find g(2x + 3), substitute 2x + 3 into the equation as the input value of x. Distribute 8 to 2x and 3, resulting in g(2x + 3) = 16x + 24 + 2 = 16x + 26.

Summary & Key Takeaways

• The content introduces function definition through the equation g(x) = 8x + 2, where x is inputted into the function and produces an output based on the equation.

• To find g(0), substitute 0 into the equation, resulting in g(0) = 2.

• To find g(-5), substitute -5 into the equation, resulting in g(-5) = -38.

• To find g(2x + 3), substitute 2x + 3 into the equation, distribute and simplify to obtain g(2x + 3) = 16x + 26.