Question

Write down a mathematical function that can be used to describe the following rule: Square the input and divide the result by two. Then add six. Use the letter t for input and the letter g to represent the function.

Answer 1

The function g(t) that squares the input t, divides by two, and then adds six is expressed as g(t) = ½t² + 6. This represents a quadratic transformation with a vertical shift.

Step-by-step explanation:

The mathematical function that describes the rule to square the input and divide the result by two, and then add six, using the letter t for input and the letter g to represent the function, can be expressed as:

g(t) = ½t² + 6

To break it down, we follow these steps:

• Square the input t: t².
• Divide that result by two: ½t² (which is the same as multiply by ½).
• Finally, add six to that result to complete the function: ½t² + 6.

This simple mathematical function is an example of a quadratic transformation, which can be graphed as a parabola that has been shifted vertically by six units.