# Lesson 11

Making a Model for Data

### Problem 1

A line $$\ell$$ is defined by the equation $$f(x) = 2x - 3$$.

1. Line $$m$$ is the same as line $$l$$, but shifted 1 unit right. What is an equation for a function $$g$$ that defines the line $$m$$?
2. Line $$n$$ is the same as line $$m$$, but shifted 2 units up. What is an equation for a function $$h$$ that defines the line $$n$$?
3. What is the relationship between $$f$$ and $$h$$?

### Solution

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(From Unit 5, Lesson 2.)

### Problem 2

The functions $$g$$ and $$f$$ are related by the equation $$g(x) = f(\text-x) + 3$$. Which sequence of transformations will take the graph of $$f$$ to the graph of $$g$$?

### Solution

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(From Unit 5, Lesson 4.)

### Problem 3

The function $$f$$ is linear. Can $$f$$ be an odd function? Explain how you know

### Solution

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(From Unit 5, Lesson 5.)

### Problem 4

Technology required. The function $$f$$ is given by $$f(x) = x^3 + 1$$. Kiran says that $$f$$ is odd because $$(\text-x)^3 = \text-x^3$$

1. Do you agree with Kiran? Explain your reasoning.
2. Graph $$f$$, and use the graph to decide whether or not $$f$$ is an odd function.

### Solution

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(From Unit 5, Lesson 6.)

### Problem 5

Here are graphs of three functions $$f$$, $$g$$, and $$h$$ given by $$f(x) = (x-1)^2$$, $$g(x) = 2(x-1)^2$$ and $$h(x) = 3(x-1)^2$$.

Identify which function matches each graph. Explain how you know.

### Solution

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(From Unit 5, Lesson 8.)

### Problem 6

Technology required. Describe how to transform the graph of $$f(x) = x^2$$ into the graph of $$g(x) = 4(3x-1)^2 + 5$$. Check your response by graphing $$f$$ and $$g$$.

### Solution

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(From Unit 5, Lesson 9.)

### Problem 7

Let $$p$$ be the price of a T-shirt, in dollars. A company expects to sell $$f(p)$$ T-shirts a day where $$f(p) = 50 - 4p$$. Write a function $$r$$ giving the total revenue received in a day.

### Solution

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(From Unit 5, Lesson 10.)

### Problem 8

A population of 80 single-celled organisms is tripling every hour. The population as a function of hours since it is measured, $$h$$, can be represented by $$g(h) =80 \boldcdot 3^h$$.

Which equation represents the population 10 minutes after it is measured?

A:

$$g(10) =80 \boldcdot 3^{10}$$

B:

$$g(0.1) =80 \boldcdot 3^{0.1}$$

C:

$$g(\frac16) =80 \boldcdot 3^\frac16$$

D:

$$g(6) =80 \boldcdot 3^6$$

### Solution

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(From Unit 4, Lesson 3.)