Exponential Functions Exploration

What is the asymptote of the graph of the exponential function f(x) = 2^x

• x = 0

• y = 0

• x = 1

• y = 1

Which transformation would result in the graph of g(x) = 3* 2^{x+1} from the graph of f(x) = 2^x

• Vertical stretch by a factor of 3 and shift left by 1 unit

• Vertical stretch by a factor of 3 and shift right by 1 unit

• Vertical stretch by a factor of 2 and shift left by 1 unit

• Vertical stretch by a factor of 2 and shift right by 1 unit

What is the domain of any exponential function f(x) = a^x where a > 0

• All real numbers

• All positive real numbers

• All negative real numbers

• ( x >= 0 )

For the exponential function f(x) = 2^x , what is the range?

• y > 0

• y >= 0

• All real numbers

• y < 0

If f(x) = 2^x and g(x) = 2^{-x} , how do the graphs of ( f ) and ( g ) relate to each other?

• They are reflections across the y-axis

• They are reflections across the x-axis

• They are the same graph

• They are translations of each other

What is the effect of adding a constant ( c ) to the function f(x) = a^x to create g(x) = a^x + c

• Horizontal shift

• Vertical stretch

• Vertical shift

• Reflection

Which of the following represents an exponential decay function?

• f(x) = 3^x

• f(x) = (1/3)^x

• f(x) = -3^x

• f(x) = 3^{-x}

What is the y-intercept of the exponential function f(x) = 5 * 2^x

• (0, 2)

• (0, 5)

• (2, 0)

• (5, 0)

If f(x) = 2^x , what is the graph if you change x to; f(x) = 2^(x-3)

• Shifted 3 units to the left

• Shifted 3 units to the right

• Shifted 3 units up

• Shifted 3 units down

What is the end behavior of the exponential function f(x) = (1/2)^x as x approaches infinity?

• f(x) approaches infinity

• f(x) approaches 0

• f(x) approaches 1

• f(x) approaches -1