1. Graphs and Graphing Utilities
Sec. 1.1
Graphs and Graphing Utilities

2. Equation Relationship between two quantities
Ex. y=7-3x (equation in 2 variables, x & y)

3. Solution or Solution Pair
Ordered pair (a,b) of equation in x & y when an equation is true when a is substituted for x & b for y
Ex (1,4) for y=7-3x

4. Graph Set of all points that are solutions Look at Ex. 1 p. 76
Look p.78 ex. 3 at misrepresentations with too few points
Calculator – Zoom Standard

5. Intercepts of a Graph Intercepts
Solution points that have zero as either the x-coordinate or y-coordinate.
(where the graph intersects that axis)

6. To find intercepts
X-int.
Let y=0 and solve
Y-int.
Let x=0 and solve

7. Ex. 3
a) y = x3-4x
b) y2 = x + 4

8. Symmetry
3 types
x-axis
y-axis
Origin
P. 80

9. Knowing the type of symmetry before graphing can help in sketching the graph.
Symmetric with respect to the y-axis
For point (x,y) on the graph, (-x,y) is also on the graph.
Check by replacing x with -x
Symmetric with respect to the x-axis
For point (x,y) on the graph (x,-y) is also on the graph
Check by replacing y with -y
Symmetric with respect to the origin
If (x,y) is on the graph (-x,-y) is also on the graph
Check by replacing both x with –x and y with -y

10. Ex. Check with respect to y-axis
y=x2-2

11. Ex. 4 Using intercepts and symmetry sketch
x-y2=1

12. Circles r – radius and center (h,k) Standard form
(x – h)2 + (y – k)2 = r2

13. Finding the equation for a circle
(3,4) is a point on the circle and the center is at (-1,2)