Exponential Shifts

Identify the vertical shift of the exponential function f(x) = 2^x - 3.

• 5

• 0

• -3

• 1

Answer explanation

The vertical shift of the exponential function f(x) = 2^x - 3 is -3. This is because the constant term -3 represents the vertical translation of the graph.

Tags

CCSS.HSF-IF.C.7E

Identify the horizontal shift of the exponential function g(x) = 2^(x+2).

• 0

• 2

• 4

• -2

Answer explanation

The horizontal shift of the exponential function g(x) = 2^(x+2) is -2, as the exponent (x+2) shifts the graph 2 units to the left.

Tags

CCSS.HSF.BF.B.3

What is the domain of the exponential function h(x) = 3^x?

• All real numbers

• No real numbers

• Only positive numbers

• Integers only

Answer explanation

The domain of the exponential function h(x) = 3^x is all real numbers. It can take any real number as an input.

What is the range of the exponential function y = 4^x?

• All negative real numbers

• Only integers

• All positive real numbers

• Only even numbers

Answer explanation

The exponential function y = 4^x has a range of all positive real numbers. This is because as x increases, the value of 4^x also increases, covering all positive values. Therefore, the correct choice is 'All positive real numbers'.

Tags

CCSS.HSF-IF.C.7E

Find the asymptote of the exponential function f(x) = 5^x - 2.

• y = 0

• y = -2

• y = 5

• y = 2

Answer explanation

The asymptote of the exponential function f(x) = 5^x - 2 is y = -2. This is because as x approaches infinity, the function approaches -2. The correct choice is y = -2.

Tags

CCSS.HSF-IF.C.7E

Find the asymptote of the exponential function g(x) = 2^(x-1).

• y = x

• y = 0

• y = 2

• y = 1

Answer explanation

The exponential function g(x) = 2^(x-1) has a horizontal asymptote at y = 0, as the exponent approaches negative infinity, the value of the function approaches 0.

Tags

CCSS.HSF-IF.C.7E

Identify the vertical shift of the exponential function f(x) = 3^x + 4.

• 2

• 3

• 5

• 4

Answer explanation

The vertical shift of the exponential function f(x) = 3^x + 4 is 4, as it is added to the function. This shifts the graph upward by 4 units.

Tags

CCSS.HSF.BF.B.3

Identify the horizontal shift of the exponential function g(x) = 2^(x-3).

• 0

• 1

• 3

• 5

Answer explanation

The horizontal shift of the exponential function g(x) = 2^(x-3) is 3, as the exponent (x-3) determines the shift. The correct choice is 3.

Tags

CCSS.HSF.BF.B.3

What is the domain of the exponential function h(x) = 4^x?

• Integers only

• No real numbers

• Only positive numbers

• All real numbers

Answer explanation

The domain of the exponential function h(x) = 4^x is all real numbers. This is because any real number can be raised to any power, including 4.

What is the range of the exponential function y = 6^x?

• All even numbers

• All positive real numbers

• Only the number 6

• All negative real numbers

Answer explanation

The exponential function y = 6^x has a range of all positive real numbers. It does not include any negative numbers or the number 6 itself.