Write y = |x| + 15 as a piecewise function.

y = -x + 15      x < 0

y = x + 15       x ≥ 0

Step-by-step explanation:

Any function under mod has a break or a point of discontinuity when the function changes it's sign.  This suggests that if the input or the value of x is greater than 2, the the function's output is positive, and if smaller than 2, then the function's output is negative.  When a function is inside the mod function or absolute value function, we only take the positive signed value. To find a working pattern of this function, we can break it into two pieces, one where the value of the function under absolute value is positive and one where the value of the function under absolute value is negative.

(I might not be right, so double-check your work )

step-by-step explanation:

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.