What is the range of h(x)?

1. For x<3, h(x)=x+2

now x+2 is an increasing line (a practical way to check, h(1)=3, h(2)=4)

the largest value it takes is at 3, not inclusive, so h(3)=5 not inclusive.

Range_1= (-∞, 5)

2. for x> or equal to 3, h(x)=-x+8, which is a decreasing line (check h(4)=4, h(5)=3 )

so this line takes its maximal value at x=3, f(3)=5 and then takes any other value to -∞.

Range_2=(-∞,5]

3. Range(h)=Range1∪Range2=(-∞, 5)∪(-∞,5]=(-∞,5]      (B)

Step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

answer: rolling a number cube and flipping a coin.

step-by-step explanation: