Question

4 from unit 5, lesson 2
function g takes a students first name for its input and gives the number of letters in the first name for its output.
a. describe the meaning of g(jada) = 4.
b. find the value of g(diego).
5 from unit 5, lesson 3
w gives the weight of a puppy, in pounds, as a function of its age, t, in months.
describe the meaning of each statement in function notation.
a. w(2) = 5
b. w(6) > w(4)
c. w(12) = w(15)

Explanation:

Problem 4

Part a

Function \( G \) takes a student's first name as input and outputs the number of letters in that name. So \( G(\text{Jada}) = 4 \) means when the input is the first name "Jada", the output (number of letters) is 4. In other words, the first name "Jada" has 4 letters.

Step 1: Identify the input

The input to function \( G \) is the first name "Diego".

Step 2: Count the letters in "Diego"

The name "Diego" has D, i, e, g, o. Let's count: 1 (D) + 1 (i) + 1 (e) + 1 (g) + 1 (o) = 5. So \( G(\text{Diego}) \) is the number of letters in "Diego", which is 5.

Function \( W \) gives the weight of a puppy (in pounds) as a function of its age \( t \) (in months). So \( W(2) = 5 \) means when the puppy's age \( t \) is 2 months, its weight \( W \) is 5 pounds.

Answer:

The first name "Jada" has 4 letters (since function \( G \) outputs the number of letters in the input first name, and here the input is "Jada" with output 4).

Part b