Explain in easy words the process of finding the range of a continuous linear function with a domain of {x|a≤x≤b}

Question

{
x
|
a
≤
x
≤
b
}
where a and b are real numbers.(2 points)
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Answer 1

To find the range of a continuous linear function over a specific domain, follow these simple steps:

Steps to Find the Range:

• Identify the Function: Start with your linear function, usually in the form y = mx + c, where m is the slope and c is the y-intercept.

• Determine the Domain: Note the limits of your domain, which is given as {x | a ≤ x ≤ b}. Here, a is the minimum value, and b is the maximum value for x.

• Calculate the Values:

  • Find y at a: Plug a into the function:
    y(a) = m*a + c.
  • Find y at b: Plug b into the function:
    y(b) = m*b + c.

• Identify the Range: The range will be the set of all y values calculated from y(a) to y(b).

  • If m (the slope) is positive:
    The range will be from y(a) to y(b).
  • If m is negative:
    The range will be from y(b) to y(a).

• Write the Final Range: Express the range in interval notation, which includes the minimum and maximum values found.

By following these steps, you can easily determine the range of your continuous linear function over the specified domain!