# Lesson 6

Features of Graphs

### 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.

1. The graph has multiple horizontal intercepts.
2. A horizontal intercept of the graph represents the time when Andre was with his bike.
3. A minimum of the graph is $$(17,1)$$.
4. The graph has two maximums.
5. 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.

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

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

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

1. Which function value is the largest: $$f(100)$$, $$g(100)$$, or $$h(100)$$?
2. Which function value is the largest: $$f(\text-100)$$, $$g(\text-100)$$, or $$h(\text-100)$$?
3. 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 $$f(x)=x^2$$.

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

### Solution

(From Unit 4, Lesson 4.)

### 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.

1. Which plant is taller at the end of 2 weeks? Explain your reasoning.
2. Which plant is taller at the end of 10 weeks? Explain your reasoning.
3. 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?
4. What does the solution to the inequality $$5 + 0.5w > 4 + 0.75w$$ represent in this situation?