Exponential and Logarithmic Transformations and Characteristics

What are the transformations of the exponential function from f(x) = 2^x to g(x) = 5(2)^x - 7?

• stretch by 5

  down 7

• compress by 5

  down 7

• stretch by 5

  up 7

• compress by 5

  up 7

What are the transformations of exponential function from f(x) = 2^x to g(x) = -2^{x + 4} + 3?

• reflect across y-axis

  stretch by 2

  right 4

  up 3

• left 4

  up 3

• reflect across x-axis

  left 4

  up 3

• stretch by 2

  right 4

  up 3

Identify whether the function, f(x) = 3(.5)^x has exponential growth or decay?

• growth

• decay

• cannot be determined

• both exponential growth and decay

What is the equation of an exponential function that is shifted 5 units to the right and down 9 units?

• f(x) = 2^{x + 5} - 9

• f(x) = 2^{x - 5} - 9

• f(x) = 2^{x - 9} - 5

• f(x) = 2^{x + 9} - 5

What are the transformations of f(x) = 2^{x + 7} + 1

• left 7

  down 1

• left 7

  up 1

• right 7

  down 1

• right 7

  up 1

When f(x) = 4^x is reflected across x-axis, vertically compressed by 2 and shifted up 3 units, what is the new equation?

• f(x) = 2(4)^x + 3

• f(x) = - 2(4)^x + 3

• f(x) = -(1/2)4^x + 3

• f(x) = 2(4)^{x + 3}

What are the transformations of f(x) = -3(4)^{x - 2} - 5

• reflect, stretch by 3

  right 2, down 5

• stretch by 3

  right 2

  down 5

• reflect, compress by 3

  left 2, down 5

• compress by 3

  left 2

  down 5

Given y = log₃x, determine the order of transformations of the function y = -log₃(x + 1).

• left 1, reflected over x-axis

• up 1, reflected over y-axis

• right 1, reflected over x-axis

• left 1, reflected over y-axis

Select all the transformations that apply when y = log₆x is changed to y = log₆(x - 1) - 5

• Horizontal shift left 1

• Horizontal shift right 1

• Vertical shift up 5

• Vertical shift down 5

When the function y = log₅x is changed to y = log ₅ (x + 1) + 1, select all the transformations that apply.

• Horizontal shift left 1

• Horizontal shift right 1

• Vertical shift up 1

• Vertical shift down 1