College Algebra Math 130 Amy Jones Lewis

Selling Balloons  Your local community group wants to raise money to fix one of the playgrounds in your area. Since balloons are popular with young children, your group decides to sell them to make money. You have bought a box of balloons for $10. You decide to sell the balloons for $1 each.  Using the variables x and y, find an algebraic equation that represents this situation.  Define each variable in your equation by writing a short phrase that describes what it represents.

Selling Balloons  Use your graphing calculator to create a graph of the function.  Describe your graph.  Where does the graph intersect the x-axis? What does the point represent in the problem?  Where does the graph intersect the y-axis? What does the point represent in the problem?

Selling Balloons  Do all the values for x and y make sense in the problem scenario?  Write an inequality to express which x values make sense in this situation.  Write an inequality to express which y values make sense.  If you ignore the scenario and think only of the algebraic function, what is the domain and range?

Exploring Transformations What effect does a change in a coefficient and/or a constants have on the graph of functions?

 Graph y = x This will be your reference line for linear functions. Include its graph in the graphs of each set of functions below.  Next graph this set of functions: y = 2x y = -2x y = 5x y = -5x y = ½ x y = -¼ x  What effects did the changing coefficients and constants have on the graph of y=x? Exploring Transformations Linear Functions

 Graph y = x This will be your reference line for linear functions. Include its graph in the graphs of each set of functions below.  Next graph this set of functions: y = x + 5 y = x - 5 y = -(x) + 5 y = -(x) - 5 y = -(x) + ½ y = -(x) - ¼  What effects did the changing coefficients and constants have on the graph of y=x? Exploring Transformations Linear Functions

 Graph y = x This will be your reference line for linear functions. Include its graph in the graphs of each set of functions below.  Next graph this set of functions: y = 2x + 5 y = 2x - 5 y = 5x + 2 y = -5x - 2 y = ¼x + 5 y = -½x – 5  What effects did the changing coefficients and constants have on the graph of y=x? Exploring Transformations Linear Functions

 Graph y = x ² This graph will be your reference graph for quadratic functions. Include its graph in the graphs of each set of functions below.  Next graph each set of functions: Set 1 Set 2 Set 3 y = -(x ² ) y = x ² + 4 y = 2x ² - 4 y = 2x ² y = x ² - 4 y = -2x ² + 4 y = -2x ² y = -(x ² ) +4 y = -2x ² – 4 y = ¼ x ² y = -(x ² ) - 4 y = ¼ x ² – 1 y = - ¼ x ² y = -(x ² ) -1 y = - ¼ x ² +1  What effects did the changing coefficients and constants have on the graph of y=x ² ? Exploring Transformations Quadratic Functions

 Graph y = x ² This graph will be your reference graph for quadratic functions. Include its graph in the graphs of each set of functions below.  Next graph each set of functions: Set 4Set 5 Set 6 y = (x + 2)² y = 2(x + 2)² y = 2(x + 2)² - 4 y = (x - 2)² y = -2(x - 2)² y = -2(x - 2)² + 4 y = -(x + 5)² y = ¼(x + 5)² y = ¼(x + 5)² + 2 y = -(x - 5)²y = - ¼(x - 5)² y = - ¼(x - 5)² - 2  What effects did the changing coefficients and constants have on the graph of y=x ² ? Exploring Transformations Quadratic Functions

 Graph this set of quadratic functions: y = x² y = x² + x – 2 y = 2x² - 4x –6 y = -2x² + 8x –6  What effects did the changing coefficients and constants have on the graph of y=x²? Exploring Transformations Quadratic Functions

 Graph y = 2 x This will be your reference graph for exponential functions.  Graph these functions with your base function. y = 2 x + 5 y = -2 x -5 y = 2 x – 5 y = 2 (x+1) – 5  What effects did the changing coefficients and constants have on the graph of y=2 x ? Test your conjectures by writing new functions, predicting what their graphs will look like, then graphing them. Exploring Transformations Exponential Functions

Five Different Representations of a Function Language TableContext GraphEquation

Homework  Explain the effects of coefficients and constants in a linear functions.  Next Class: Wednesday, October 20th