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

Tags

CCSS.HSF-IF.C.7E

• 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.

Tags

CCSS.HSF-IF.C.7E

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

Tags

CCSS.HSF.LE.A.2

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

Tags

CCSS.HSF.LE.A.2

• 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

Tags

CCSS.HSF-IF.C.7E

• 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