1. Bellringer (7 minutes) Making use of the following:
What is your domain?
What is your range?
What are your x- and y-intercepts?

2. Liberal Arts Math 1
16 January 2019

3. announcements It’s time for a quiz…not today, don’t get nervous
It’ll probably be Friday of next week
I’ll know for certain by Friday after the department meeting

4. Functions and graphs – domain and range

5. Functions and graphs – domain and range
Now, I’m going to put the previous graph as a word problem:
Famous Amos is a cookie company that has been able to measure its profit to production in terms of the following graph.
How many cookies would the company have to make in order to break even?

6. Functions and graphs – domain and range
If I “break even”, then my profit = 0.
So I’m looking for places on the graph where profit equals zero.  x-intercepts

7. Functions and graphs – domain and range

8. Functions and graphs – domain and range
How about if I’m looking for my maximum profit?
I’m looking for the highest place(s) on the graph.  the upper range

9. Functions and graphs – domain and range

10. Slope Equations
Now that we’ve looked at some graphs, let’s look at some actual equations of graphs
There are three possible forms of the slope I want to point out (each has pros and cons):
Slope-intercept form: y = mx + B  most-commonly used in Algebra
Standard form: Ax + By = C
Point-slope form: y – yP = m(x - xP)  oddly easy, but still useful

11. Slope equations y = mx + B Let’s start with slope-intercept form
Most problems will either give you this form, or require you convert into this form
So, let’s start with a simple problem…

12. Slope equations – slope-intercept form
What is the equation of a line that passes through (2, 3) and has a slope of m = 6?

13. Slope equations – slope-intercept form
What is the equation of a line that passes through (2, 3) and (6, 11)?

14. Slope-equations – slope-intercept form
What is the equation of a line that passes through (3, – 7) and (– 6, 11)?