Calculus - P.1 Graphs and Models

Question 0

Intercepts

Answer 0

Where the graph crosses the x-axis or y-axis

Question 1

Point-Plotting

Answer 1

A. Table or T-chart to generate solution points or use transformation of parent graph
B. Plot points
C. Connect points with smooth curve

Question 2

X-intercepts

Answer 2

X-int: (a,0)

Let y=0 and solve for x

Question 3

Y-intercepts

Answer 3

Y-int: (0,b)

Let x=0, solve for y

Question 4

Y-axis symmetry

Answer 4

Any point, (a,b), on the graph will have a matching point (-a,b) on the graph.
Test => f(-x)=f(x)

Question 5

X-axis symmetry

Answer 5

If a point (a,b) is on the graph, then the point (a,-b) is also on the graph
Test => f(x)=_+f(x)
For each value of x, there are 2 values of y
Change y to -y will not change the function y=-y or f(x)=-f(x)

Question 6

Symmetric about the origin

Answer 6

If the point (a,b) is on the graph, (-a,-b) will also be on the graph
Test =>
f(-x)=-f(x)
f(-x)=-y

Question 7

Points of intersection between two graphs

Answer 7

1. Set one = to the other and solve. Plug answer into first equation to get both x and y => (x,y)
2. Solve as a System of equation => By substitution
3. Graph is indicated

Note: In some cases you may also solve by elimination

Question 8

Use calculator two find points of intersection between two graphs

Answer 8

1. Place functions in any, and y2
2. Calc(2nd Trace) => Intersect #5
3. Enter, enter, enter => write down the point
   Trace the next point and repeat if necessary