Question

ection: __1
precalculus
1.1 exit ticket: (complete the questions independently and quietly)

1. in your own words, what is a function?

(handwritten: a function is the relationship between the two variables)

1. let f(x) = 2x + 3. find f(5)
2. apply: \why can height → age not be a function?\

Explanation:

Question 2 Solution:

Step1: Substitute x = 5 into f(x)

To find \( f(5) \) for the function \( f(x) = 2x + 3 \), we replace \( x \) with 5 in the function. So we get \( f(5)=2\times5 + 3 \).

Step2: Calculate the result

First, calculate the multiplication: \( 2\times5 = 10 \). Then, add 3 to the result: \( 10+3 = 13 \).

Answer:

\( f(5)=13 \)

Question 1 Explanation (for reference, as it's a descriptive question):

A function is a rule that assigns to each input (usually called the independent variable, like \( x \)) exactly one output (the dependent variable, like \( f(x) \)). It describes a relationship where for every valid input, there's a unique corresponding output.

Question 3 Explanation (for reference, as it's a conceptual question):

For a relationship to be a function, each input must have exactly one output. In the relationship "height → age", a single height (input) can correspond to multiple ages (outputs). For example, many different - aged people can have the same height (e.g., a 10 - year - old and a 12 - year - old might both be 5 feet tall). So since one input (height) can have more than one output (age), it does not satisfy the definition of a function.