Math Studio College Algebra

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1 - Studio College Algebra Kansas State University August 31, 2016

2 Format of a Linear Function Terminology: What are intercepts on the graph of a function?

3 Format of a Linear Function Terminology: What are intercepts on the graph of a function? Slope Intercept Form: f (x) = mx + b. Question: What do m and b represent?

4 Format of a Linear Function Terminology: What are intercepts on the graph of a function? Slope Intercept Form: f (x) = mx + b. Question: What do m and b represent? Point Slope Form: y y 0 = m(x x 0 ). Question: What do m and (x 0, y 0 ) represent?

5 A company is offering a closeout deal on some custom T-shirts (more specifically, the company only has 200 shirts left in the color royal purple.) The initial fee for setting up a shirt with the slogan Every Wildcat A Mathematician is $75. Then, the cost for making between 0 and 200 shirts is $20 per shirt.

6 A company is offering a closeout deal on some custom T-shirts (more specifically, the company only has 200 shirts left in the color royal purple.) The initial fee for setting up a shirt with the slogan Every Wildcat A Mathematician is $75. Then, the cost for making between 0 and 200 shirts is $20 per shirt. a) Write a linear function C(x) describing the total cost of producing shirts.

7 A company is offering a closeout deal on some custom T-shirts (more specifically, the company only has 200 shirts left in the color royal purple.) The initial fee for setting up a shirt with the slogan Every Wildcat A Mathematician is $75. Then, the cost for making between 0 and 200 shirts is $20 per shirt. a) Write a linear function C(x) describing the total cost of producing shirts. b) Find the y-intercept of C(x). What is its meaning?

8 A company is offering a closeout deal on some custom T-shirts (more specifically, the company only has 200 shirts left in the color royal purple.) The initial fee for setting up a shirt with the slogan Every Wildcat A Mathematician is $75. Then, the cost for making between 0 and 200 shirts is $20 per shirt. a) Write a linear function C(x) describing the total cost of producing shirts. b) Find the y-intercept of C(x). What is its meaning? c) State the slope of C(x). What is its meaning in context of the situation?

9 A company is offering a closeout deal on some custom T-shirts (more specifically, the company only has 200 shirts left in the color royal purple.) The initial fee for setting up a shirt with the slogan Every Wildcat A Mathematician is $75. Then, the cost for making between 0 and 200 shirts is $20 per shirt. a) Write a linear function C(x) describing the total cost of producing shirts. b) Find the y-intercept of C(x). What is its meaning? c) State the slope of C(x). What is its meaning in context of the situation? d) What is the domain of C(x) in context of the situation?

10 A company is offering a closeout deal on some custom T-shirts (more specifically, the company only has 200 shirts left in the color royal purple.) The initial fee for setting up a shirt with the slogan Every Wildcat A Mathematician is $75. Then, the cost for making between 0 and 200 shirts is $20 per shirt. a) Write a linear function C(x) describing the total cost of producing shirts. b) Find the y-intercept of C(x). What is its meaning? c) State the slope of C(x). What is its meaning in context of the situation? d) What is the domain of C(x) in context of the situation? e) What is the domain of C(x) if context is irrelevant?

11 A company is offering a closeout deal on some custom T-shirts (more specifically, the company only has 200 shirts left in the color royal purple.) The initial fee for setting up a shirt with the slogan Every Wildcat A Mathematician is $75. Then, the cost for making between 0 and 200 shirts is $20 per shirt. a) Write a linear function C(x) describing the total cost of producing shirts. b) Find the y-intercept of C(x). What is its meaning? c) State the slope of C(x). What is its meaning in context of the situation? d) What is the domain of C(x) in context of the situation? e) What is the domain of C(x) if context is irrelevant? f) What is C(50) in context of the situation?

12 With respect to the Wildcat t-shirt function, how many t-shirts must be sold by the company in order for them to have revenue of $475?

13 Marginal Profit This term refers to the additional profit gained from selling 1 more unit of product (the same idea can be applied to cost, revenue, and BASEBALL, as you ll discover is studio this week!) Question: If a profit function is linear, what is the marginal profit?

14 Absolute Value Functions Definition of Absolute Value Function { x, x 0 f (x) = x = x, x < 0

15 Absolute Value Equations Solve: 3x 5 = 7

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