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Basic Functions
Basic Functions
• Linear and Exponential Functions
• Power Functions
• Logarithmic Functions
• Trigonometric Functions
A population of 200 worms increases at the rate of 5 worms per day. How many worms are there after a fifteen days?
Linear Function
Linear Functions
Slope m=rise/run
Change on y when x increases by 1
Y intercept or value when x=0
Exercise
• Find the equation of the line passing through the points (-2,1), (4,5)
• Point: • Slope:
• Point-Slope form• Slope-Y intercept form
Exponential Growth
A population of 200 worms increases at the rate of 5% per day. How many worms are there after fifteen days?
Exponential Growth
• Population of Mexico City since 1980 (t=0)
t (years after 1980
0 1 2 3
P(t) (in millions)
67.38 70.9187821 72.7626705 74.6544999
Is this a linear function?
t (years after 1980
0 1 2 3
P(t) (in millions)
67.38 70.9187821 72.7626705 74.6544999
Equation from Tablet (years after
19800 1 2 3
P(t) (in millions)
67.38 70.9187821 72.7626705 74.6544999
Initial Population
t=0
Grows at 2.6% per year (100%+2.6% next period)
1.026 = growth factor1=1+0.026
What is the doubling time?
1. Shape2. Domain3. End behavior 4. Intercepts with coordinate axes5. Compare them– Common domain– Intercepts – Dominance
What do you need to know about the basic functions?
Power Functions
Positive Even Powers
1. Shape2. Domain3. End behavior 4. Intercepts with
coordinate axes
Positive Odd Powers
1. Shape2. Domain3. End behavior 4. Intercepts with
coordinate axes5. Compare them– Intercepts – Dominance
Negative Even Powers
1. Shape2. Domain3. End behavior 4. Intercepts with
coordinate axes5. Compare them– Intercepts – Dominance
Negative Odd Powers
1. Shape2. Domain3. End behavior 4. Intercepts with
coordinate axes5. Compare them– Intercepts – Dominance
Positive Even Roots
1. Shape2. Domain3. End behavior 4. Intercepts with
coordinate axes5. Compare them– Intercepts – Dominance
Positive Odd Roots
1. Shape2. Domain3. End behavior 4. Intercepts with
coordinate axes5. Compare them– Intercepts – Dominance
Exponential Growth
1. Shape2. Domain3. End behavior 4. Intercepts with
coordinate axes5. Compare them– Intercepts – Dominance
Exponential Decay
1. Shape2. Domain3. End behavior 4. Intercepts with
coordinate axes5. Compare them– Intercepts – Dominance
Natural Log Function
1. Shape2. Domain3. End behavior 4. Intercepts with
coordinate axes5. Compare them– Intercepts – Dominance
Sine and Cosine
COMPARING FUNCTIONS
Consider the functions For which values in their common domain is
• Toward the end points of the common domain which of the two functions dominate?
Common domainGraphical SolutionAlgebraic Solution number line
Dominance
• Comparing functions toward the end points of their common domains
