Asymptote

A line that a graph gets closer and closer to, but never crosses or touches

x-intercept – the point at which the line intersects the x-axis at (x, 0)

y-intercept – the point at which the line intersects the y-axis at (0, y)

Intercepts

Increasing & Decreasing

MOVE LEFT TO RIGHT !If your finger is going up, the graph is INCREASING

If your finger is going down, the graph is DECREASING

If your finger doesn’t go up or down…then the graph is CONSTANT

Maximum – the highest point of a function

Minimum – the lowest point of a function

Max/Min

Characteristics

1. Domain:__(∞, ∞ )____

2. Range:__(-4, ∞ )_______

3. Intercepts: _x:(0,0), y: (0,0)___

4. Inc or Dec?__Inc____

5. Max or Min?______

6. Asymptote:_y = -4__

An exponential function like this really doesn’t have a max or min. The asymptote is approached but never reached. ∞ is not measureable and the max can’t be identified.

Characteristics1. Domain:________

2. Range:_________

3. x-intercept:_______

4. y-intercept:_______

5. Inc or Dec?______

6. Max or Min?______

7. Asymptote: __________

Characteristics1. Domain:________

2. Range:_________

3. x-intercept:_______

4. y-intercept:_______

5. Inc or Dec?______

6. Max or Min?______

7. Asymptote: __________

A taxi company in Atlanta charges $2.75 per ride plus $1.50 for every mile driven. Write the equation for the line, and determine the key features of this function.

1. Equation: _______

Word problem

2. Domain: _______

3. Range: ________

4. Intercepts: _____

5. Max or Min: ____

6. Inc or Dec: _____

7. Discrete or Cont:__

A pendulum swings to 90% of its height on each swing and starts at a height of 80 cm. The height of the pendulum in centimeters, y, is recorded after x number of swings. Write the equation, and determine the key features of this function.

1. Equation: _______

Word problem

2. Domain: _______

3. Range: ________

4. Intercepts: _____

5. Max or Min: ____

6. Inc or Dec: _____

7. Discrete or Cont:__

Classwork/Homework7 Problems