Question

Evaluate the piecewise function f(x) = x+4, x<5; 8, 5≤x<7; 2x−1, 7≤x≤10 at various intervals.

a) Determine f(x) for x values less than 5.
b) Calculate f(x) when x lies between 5 and 7.
c) Find f(x) for x values between 7 and 10.
d) Solve for f(x) at different x intervals as per the function.

Answer 1

To evaluate the piecewise function at various intervals, select the appropriate segment for the given x value, substitute x into the equation, and calculate f(x). For x values less than 5, use f(x) = x+4; for x between 5 and 7, f(x) is constantly 8; for x between 7 and 10, use f(x) = 2x-1.

Step-by-step explanation:

The piecewise function in question is defined as f(x) = x+4 for x < 5, f(x) = 8 for 5≤x<7, and f(x) = 2x−1 for 7≤x≤10.

• For x values less than 5, f(x) is calculated as x+4. Any x that is less than 5, plug it into the function f(x) = x+4 to find the corresponding f(x) value.
• When x lies between 5 and 7, the function value is a constant 8. Regardless of the x-value in this interval, f(x) will be 8.
• For x values between 7 and 10, f(x) is given by 2x-1. To find f(x), multiply the x value by 2 and subtract 1.

To solve for f(x) at different x intervals as per the function:

1. Evaluate the appropriate piecewise segment based on the value of x provided.
2. Use substitution to replace x with the given value in the segment's equation.
3. Calculate the resultant value to find f(x).