EXPONTENTIAL FUNCTIONS

PARENT GRAPH AND TABLE

SYMBOLIC FORM

EXPLANATION OF "A"

• It reflects the line across the x-axis if it is negative
• It either shrinks (goes up slower) or stretches (goes up faster) the graph
• It multiplies the y values by itself on the table

EXAMPLES OF CHANGES IN A

EXPLANATION OF "H"

• It translates the graph left or right on the x-axis
• To translate left; add
• To translate right; subtract
• It effects the x values on the table

EXAMPLES OF CHANGES IN H

EXPLANATION OF "K"

• It is the y value that the asymptote approaches
• It translates the graph up and down on the y-axis
• To translate down; subtract
• To translate up; add
• It effects the y values on the table

EXAMPLES OF CHANGES IN K

TRANSORMATIONS

• If the graph moves to the left, add the number of places it moves to the exponent
• If the graph moves to the right, subtract the number of places it moves from the exponent
• If the graph moves down, make k negative (subtract)
• If the graph moves up, make k positive (add)

FUNCTION QUESTIONS

• Is it a function?: yes; every x has 1 y
• Domain: all real numbers, Range: (0,infinity)
• Increasing: (-infinity,infinity) Decreasing: never
• As x --> infinity, y --> infinity; As x--> -infinity, y --> 0
• No critical points

FUNCTION QUESTIONS CONTINUED

• Intercepts: (0,1)
• Is its inverse a function?: yes; every y has 1 x
• Positive: (-infinity, infinity) Negative: never

QUESTIONS?