Pre-Calculus Homework - Section 3.1 Exponential Functions

• Yes, the following function is an exponential Function where a = 3 (initial value) and b = 2 (constant multiplier)

• No, the following function is not an exponential function

• Yes, the following function is an exponential Function where a = 2 (initial value) and b = 3 (constant multiplier)

• Yes, the following function is an exponential Function where a = -5 (initial value) and b = 3 (constant multiplier)

• No, the following function is not an exponential function because x is not in the exponent

• Yes, the following function is an exponential Function where a = 3 (initial value) and b = -5 (constant multiplier)

• Yes, the following function is an exponential Function where a = 5 (initial value) and b = 1/2 (constant multiplier)

• No, the following function is not an exponential function because a < 1

• Yes, the following function is an exponential Function where a = 1/2 (initial value) and b = 5 (constant multiplier)

• 1. H.A. = 1

  2. y-intercept = (0, -1)

  3. *Increases exponentially for x > 0 and approaches y = -1 as x approaches -infinity

• 1. H.A. = -1

  2. y-intercept = (0, 1)

  *Increases exponentially for x > 0 and approaches y = -1 as x approaches -infinity

• 1. H.A. = -1

  2. y-intercept = (0,-1)

  *Increases exponentially for x > 0 and approaches y = -1 as x approaches -infinity

• 1. H.A. = 1

  2. y-intercept = (0,1)

  3. *Increases exponentially for x > 0 and approaches y = -1 as x approaches -infinity

• 1. H.A. = 2

  2. y-intercept = (0,-2.5)

  3. End Behavior = when x > 0 then the function decreases exponentially, when x < 0 then the function increases above the H.A.

• 1. H.A. = -2

  2. y-intercept = (0,-2.5)

  3. End Behavior = when x > 0 then the function decreases exponentially, when x < 0 then the function increases above the H.A.

• 1. H.A. = 2

  2. y-intercept = (0,2.5)

  3. End Behavior = when x > 0 then the function decreases exponentially, when x < 0 then the function increases above the H.A.

• 1. H.A. = 2

  2. y-intercept = (0,2.5)

  3. End Behavior = when x < 0 then the function decreases exponentially, when x > 0 then the function increases above the H.A.

find the exponential function that passes through the given points (1,4) (3,36)

Find the exponential function that passes through the points (0,16) (2, 144)

• 1. H.A. = -2

  2. Shifted 4 units left and 2 units down

  3. Behavior: as x approaches infinity then the function grows exponentially, as x approaches -infinity then it approaches the horizontal asymptote

• 1. H.A. = -2

  2. Shifted 2 units left and 4 units down

  3. Behavior: as x approaches infinity then the function grows exponentially, as x approaches -infinity then it approaches the horizontal asymptote

• 1. H.A. = -2

  2. Shifted 4 units left and 2 units down

  3. Behavior: as x approaches infinity then the function grows exponentially, as x approaches -infinity then it grows exponentially

• 1. H.A. = 2

  2. Shifted 4 units left and 2 units down

  3. Behavior: as x approaches infinity then the function grows exponentially, as x approaches -infinity then it approaches the horizontal asymptote

• 1. H.A. = -2

  2. Transformation = vertical compression by 1/2, horizontal shift 2 units right, vertical shift 2 units down,

  3. End Behavior = as x approaches +infinity then the graph approaches -2, as x approaches -infinity then the graph exponentially grows

• 1. H.A. = -2

  2. Transformation = vertical compression by 1/2, horizontal shift 2 units left, vertical shift 2 units upward,

  3. End Behavior = as x approaches -infinity then the graph approaches -2, as x approaches infinity then the graph exponentially grows

• 1. H.A. = 2

  2. Transformation = vertical compression by 1/2, horizontal shift 2 units right, vertical shift 2 units upward,

  3. End Behavior = as x approaches -infinity then the graph approaches -2, as x approaches infinity then the graph exponentially grows

• 1. H.A. = -2

  2. Transformation = vertical compression by 1/2, horizontal shift 2 units right, vertical shift 2 units down,

  3. End Behavior = as x approaches -infinity then the graph approaches -2, as x approaches infinity then the graph exponentially grows

• x = 2

• x = 4

• x = 6

• x = 8