# Lesson 6

Features of Graphs

- Let’s use graphs of functions to learn about situations.

### Problem 1

This graph represents Andre’s distance from his bicycle as he walks in a park.

Decide whether the following statements are true or false.

- The graph has multiple horizontal intercepts.
- A horizontal intercept of the graph represents the time when Andre was with his bike.
- A minimum of the graph is \((17,1)\).
- The graph has two maximums.
- About 21 seconds after he left his bike, he was the farthest away from it, at about 8.3 feet.

### Problem 2

The graph represents the temperature in degrees Fahrenheit as a function of time.

Tell the story of the temperature throughout the day.

Identify the maximum and minimum of the function and where the function is increasing and decreasing.

### Problem 3

Match each feature of the situation with a corresponding statement in function notation.

### Problem 4

Here are the equations that define three functions.

\(f(x)=4x-5\)

\(g(x)=4(x-5)\)

\(h(x)=\frac x 4 - 5\)

- Which function value is the largest: \(f(100)\), \(g(100)\), or \(h(100)\)?
- Which function value is the largest: \(f(\text-100)\), \(g(\text-100)\), or \(h(\text-100)\)?
- Which function value is the largest: \(f(\frac{1}{100})\), \(g(\frac{1}{100})\), or \(h(\frac{1}{100})\)?

### Problem 5

Function \(f\) is defined by the equation \(f(x)=x^2\).

- What is \(f(2)\) ?
- What is \(f(3)\) ?
- Explain why \(f(2)+f(3) \ne f(5)\).

### Problem 6

Priya bought two plants for a science experiment. When she brought them home, the first plant was 5 cm tall and the second plant was 4 cm. Since then, the first plant has grown 0.5 cm a week and the second plant has grown 0.75 cm a week.

- Which plant is taller at the end of 2 weeks? Explain your reasoning.
- Which plant is taller at the end of 10 weeks? Explain your reasoning.
- Priya represents this situation with the equation \(5 + 0.5w = 4 + 0.75w\), where \(w\) represents the end of week \(w\). What does the solution to this equation, \(w = 4\) represent in this situation?
- What does the solution to the inequality \(5 + 0.5w > 4 + 0.75w\) represent in this situation?