# Lesson 2

Understanding Points in Situations

- Let’s understand points on a function in a situation.

### 2.1: A Day of Temperature

The temperature for a city is a function of time after midnight. The graph shows the values on a particular spring day.

- What does the point on the graph where \(x = 15\) mean?
- What is the temperature at 5 p.m.?
- What is the hottest it gets on this day?
- What is the coldest it gets on this day?

### 2.2: What Happens to -2?

For each of these equations, find the value of \(y\) when \(x = \text{-}2\).

- \(y = 3x - 4\)
- \(y = 10 - 2x\)
- \(y = \frac{3}{2}x + 5\)
- \(y = 2(x - 1) + 4\)
- \(y = \text{-}x + 19\)
- \(y = \frac{x - 3}{8}\)
- \(y = 0.3x + 5\)

### 2.3: It’s Heating Up!

The temperature, in degrees Fahrenheit, of a scientific sample being warmed steadily as a function of time in seconds after the sample is put in a machine can be represented by the equation \(y = 2.1x + 86\).

- What does it mean when \(x = 2\)?
- What is the temperature in that situation?
- What does it mean when \(y = 122\)?
- A graph of this equation goes through the point \((60,212)\). What does that mean?
- Give 2 values for \(x\) that do not make sense. Explain your reasoning.
- Give 2 values for \(y\) that do not make sense. Explain your reasoning.