Question

Part A: Write the piecewise-defined function that represents the situation.

a) C(x) = 18, for x 20; C(x) = 12, for 20 < x 50; C(x) = 9, for 50 < x < 100; C(x) = 5, for 100 x 200; C(x) = 3, for x > 200
b) C(x) = 18x, for x 20; C(x) = 12x, for 20 < x 50; C(x) = 9x, for 50 < x < 100; C(x) = 5x, for 100 x 200; C(x) = 3x, for x > 200
c) C(x) = 18x, for x < 20; C(x) = 12x, for 20 x < 50; C(x) = 9x, for 50 x < 100; C(x) = 5x, for 100 x < 200; C(x) = 3x, for x 200
d) C(x) = 18, for x < 20; C(x) = 12, for 20 x < 50; C(x) = 9, for 50 x < 100; C(x) = 5, for 100 x < 200; C(x) = 3, for x 200

Answer 1

The correct answer is b) C(x) = 18x, for x < 20; C(x) = 12x, for 20 < x < 50; C(x) = 9x, for 50 < x < 100; C(x) = 5x, for 100 < x < 200; C(x) = 3x, for x > 200. The function C(x) is multiplied by x for each specified interval of x values.

Step-by-step explanation:

The correct answer is b) C(x) = 18x, for x < 20; C(x) = 12x, for 20 < x < 50; C(x) = 9x, for 50 < x < 100; C(x) = 5x, for 100 < x < 200; C(x) = 3x, for x > 200

1. C(x) = 18x, for x < 20 means that for any value of x less than 20, the function C(x) will equal 18 times that value of x.
2. The same logic applies to the rest of the intervals specified in the function: for x values between 20 and 50, C(x) will equal 12 times x; for x values between 50 and 100, C(x) will equal 9 times x; for x values between 100 and 200, C(x) will equal 5 times x; and for x values greater than 200, C(x) will equal 3 times x.