Exponential Vertical and Horizontal Translations

The graph shows f(x) = (1/2)^x and its translation, g(x).

Which describes the translation of f(x) to g(x)?

• translation of four units up

• translation of five units up

• translation of four units to the right

• translation of five units to the right

The graphs of f(x) = 10^x and its translation, g(x), are shown.

What is the equation of g(x)?

• g(x) = 10^x-3

• g(x) = 10^x+3

• g(x) = 10^x – 3

• g(x) = 10^x +3

The graphs of f(x) = 5^x and its translation, g(x), are shown on the graph.

What is the equation of g(x)?

• g(x) = 5^x-9

• g(x) = 5^x-10

• g(x) = 5^x – 9

• g(x) = 5^x – 10

Which is the graph of g(x) = 2^x-1 + 3?

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Which is the graph of g(x) = (0.5)^x+3 – 4?

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The graph shows that f(x) = 3^x is translated horizontally and vertically to create the function g(x) = 3^x-h +k

What is the value of h?

• -2

• -1

• 1

• 2

Which set of steps will translate f(x) = 6^x to g(x) = 6^x-5 – 7?

• Shift f(x) = 6^x five units to the left and seven units up.

• Shift f(x) = 6^x five units to the right and seven units down.

• Shift f(x) = 6^x seven units to the right and five units up.

• Shift f(x) = 6^x seven units to the left and five units down.

What is the domain of f(x) = 3^{x – 2}?

• {x | x > 0}

• {x | x < 0}

• {x | x = 0}

• {x | x is a real number}

What is the domain of f(x) = 5^x – 7?

• {x | x > –7}

• {x | x < –7}

• {x | x > 0}

• {x | x is a real number}

What is the range of f(x) = 3^x + 9?

• {y | y < 9}

• {y | y > 9}

• {y | y > 3}

• {y | y < 3}