6.5 FORMATIVE: Transformations of Exponential Functions

Front

What is the transformation of the function y = 2^x when it becomes y = 2^(x+3) - 6?

Back

The function is shifted left 3 units and down 6 units.

Front

How does the function f(x) = 3^x - 4 compare to the basic function g(x) = 3^x?

Back

The function is shifted down 4 units.

Front

What function reflects y = (1/2)^x over the x-axis?

Back

y = - (1/2)^x.

Front

What equation represents a transformation of y = 2^x to the right by 3 units?

Back

y = 2^(x - 3).

Front

What transformations occur to f(x) = 2^x when it becomes g(x) = -2^(x+3) - 6?

Back

The function reflects over the x-axis, shifts left 3 units, and down 6 units.

Front

What does it mean for a function to reflect over the x-axis?

Back

The output values of the function are negated, changing the sign of y.

Front

If y = 2^x is transformed to y = 2^(x-2), what is the transformation?

Back

The function is shifted right 2 units.

Front

What is the effect of adding a positive constant to an exponential function?

Back

It shifts the graph upward.

Front

What is the effect of subtracting a constant from an exponential function?

Back

It shifts the graph downward.

Front

How does the transformation y = -3^x differ from y = 3^x?

Back

The first function reflects over the x-axis.