Foundations for Functions Chapter 1

1-1 Exploring Functions Terms you need to know – Transformation, Translation, Reflection, Stretch, and Compression

Perform the transformations to the point (-1,2). What is the new coordinate? 1a. 3 units left b. 4 units right, 3 units up

Use a table to transform 2a. 2 units up b. Across x-axis

Use a table to perform a 3a. vertical stretch of factor 2 b. horizontal compression of factor ½.

1-2 Introduction to Parent Functions Terms you need to know – Parent Function, Linear, Quadratic, Cubic, and Square root

Identify the parent function and graph on the calculator. Describe the transformation. State Domain and Range

Given the following points, graph the data and identify the parent function. Describe the transformation that bests fits the data.

Graph the relationship from year to sales in millions of dollars. Which parent function best describes it? Use graph to estimate when sales reach $10 million. YearSales (million$)

1-3 Transforming Linear Functions

Let g(x) be the indicated transformation of f(x). Write the rule for g(x). x-202 f(x)012 2.

3. Let g(x) be a horizontal compression of f(x) = - x+4 by a factor of ½. Write the rule and graph it.

4. Let g(x) be a horizontal shift of f(x) = 3x left 6 units followed by a horizontal stretch of factor 4. Write the rule for g(x)

5.The golf team is selling T-shirts for a fundraiser. The function R(n) = 7.5n represents the teams revenue in dollars and the number of shirts sold (n). a. The team paid $60 for the shirts. Write a function P(n) for the teams profit. b. Graph both functions and describe the transformation applied.

1-4 Curve fitting with Linear models Terms you need to know – regression, correlation, line of best fit, correlation coefficient

Positive correlation – y tends to __________ as x __________. Negative correlation – y tends to __________ as x __________. Relatively no correlation – no ________ pattern.

x y Draw the scatterplot. Name the type of correlation, sketch the line of best fit, and find its equation.

Example: Constructing a Scatter Plot A marketing manager conducted a study to determine whether there is a linear relationship between money spent on advertising and company sales. The data are shown in the table. Display the data in a scatter plot, determine correlation, find the correlation coefficient, and the line of best fit using the calculator. Do a screen sketch. Advertising expenses, ($1000), x Company sales ($1000), y

Solution: Constructing a Scatter Plot Using Technology Enter the x-values into list L 1 and the y-values into list L 2. Use Stat Plot to construct the scatter plot. STAT > Edit…STATPLOT From the scatter plot, it appears that the variables have a____________linear correlation.

Predict sales if $2500 was spent in advertising.