5.2 Exponential Transformations Lesson Check

Front

What is the transformation of the function if it reflects across the line y=0?

Back

Reflection across the line y=0 means the graph is flipped over the x-axis.

Front

How does the function y=2(4)^(x-3)+1 transform the original function y=4^x?

Back

The graph is vertically stretched by a factor of 2, shifted right 3 units, and shifted up 1 unit.

Front

What is the asymptote of the function y=4(5)^x?

Back

The asymptote is y = 0.

Front

What effect does adding a constant 'k' have in the function y=a(b)^x+k?

Back

Adding a constant 'k' results in a vertical translation of the graph.

Front

What is the y-intercept of the function y=4(5)^x?

Back

The y-intercept is (0, 4).

Front

Define vertical translation in the context of exponential functions.

Back

Vertical translation occurs when a constant is added or subtracted from the function, shifting the graph up or down.

Front

What does a horizontal translation to the right by 3 units indicate in an exponential function?

Back

It indicates that the function is shifted 3 units to the right on the x-axis.

Front

Explain the significance of the base 'b' in the exponential function y=a(b)^x.

Back

The base 'b' determines the growth or decay rate of the exponential function.

Front

What is the effect of a negative coefficient in front of an exponential function?

Back

A negative coefficient reflects the graph across the x-axis.

Front

How does the transformation y=4(5)^(x+2) differ from y=4(5)^x?

Back

The transformation y=4(5)^(x+2) shifts the graph left 2 units.