Question

name: date:
goal: understand what function notation means by connecting inputs, rules, and outputs.
part a: the function machine
a machine takes a number, multiplies it by 2, then adds 3.
input output
1 5
3 9
0 3
what does the machine do to the number each time?
part b: writing the rule
we name the machine f. the rule is written as:
f(x) = 2x + 3

1. f(1) =
2. f(3) =

sentence frame:
f(1) means i replace x with __, so the answer is

Explanation:

For \( f(3) \):

Step1: Identify the function rule

The function is given by \( f(x) = 2x + 3 \). We need to find \( f(3) \), so we substitute \( x = 3 \) into the function.

Step2: Substitute \( x = 3 \) into \( f(x) \)

Substitute \( x = 3 \) into \( f(x) = 2x + 3 \):
\( f(3) = 2(3) + 3 \)

Step3: Simplify the expression

First, calculate \( 2(3) = 6 \), then add 3: \( 6 + 3 = 9 \).

Answer:

\( f(3) = 9 \)