# Lesson 3

More Movement

### Problem 1

Here is a graph of $$f$$ and a graph of $$g$$. Express $$g$$ in terms of $$f$$ using function notation.

### Problem 2

Tyler leaves his house at 7:00 a.m. to go to school. He walks for 20 minutes until he reaches his school, 1 mile from his house. The function $$d$$ gives the distance $$d(t)$$, in miles, of Tyler from his house $$t$$ minutes after 7:00 a.m.

1. Explain what $$d(5)=0.25$$ means in this context.
2. On snowy days, Tyler’s school has a 2 hour delayed start time (120 minutes). The function $$s$$ gives Tyler’s distance $$s(t)$$, in miles, from home $$t$$ minutes after 7:00 a.m. with a 120 minute delayed start time. If $$d(5)=0.25$$, then what is the corresponding point on the function $$s$$?
3. Write an expression for $$s$$ in terms of $$d$$.
4. A new function, $$n$$, is defined as $$n(t)=d(t + 60)$$ explain what this means in terms of Tyler’s distance from school.

### Problem 3

Technology required. Here are the data for the population $$f$$, in thousands, of a city $$d$$ decades after 1960 along with the graph of the function given by $$f(d) = 25 \boldcdot (1.19)^d$$. Elena thinks that shifting the graph of $$f$$ up by 50 will match the data. Han thinks that shifting the graph of $$f$$ up by 60 and then right by 1 will match the data.

1. What functions define Elena's and Han's graphs?
2. Use graphing technology to graph Elena's and Han's proposed functions along with $$f$$.
3. Which graph do you think fits the data better? Explain your reasoning.

### Problem 4

Here is a graph of $$y = f(x+2)-1$$ for a function $$f$$.

Sketch the graph of $$y = f(x)$$.

### Problem 5

Describe how to transform the graph of $$f$$ to the graph of $$g$$:

1. using only translations
2. using a reflection and a translation

### Solution

Here is a graph of function $$f$$ and a graph of function $$g$$. Express $$g$$ in terms of $$f$$ using function notation.