Review: Transformation of the graph of Exponential Function

Front

What is the basic form of an exponential function?

Back

The basic form of an exponential function is y = a(b)^x, where 'a' is a constant, 'b' is the base (b > 0), and 'x' is the exponent.

Front

What does a horizontal shift of a graph indicate?

Back

A horizontal shift indicates that the graph of the function has been moved left or right along the x-axis.

Front

How does the equation y = 2^(x-3) transform the basic function y = 2^x?

Back

It represents a horizontal shift of 3 units to the right.

Front

What is the effect of multiplying an exponential function by a constant greater than 1?

Back

It vertically stretches the graph of the function.

Front

What transformation occurs when an exponential function is reflected across the line y=0?

Back

The graph is reflected over the x-axis.

Front

What does adding a constant 'k' to the exponential function y = a(b)^x do?

Back

It results in a vertical translation of the graph.

Front

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

Back

A negative base results in a non-function, as it does not pass the vertical line test.

Front

How does the base 'b' in the function y = a(b)^x affect the growth or decay of the function?

Back

If b > 1, the function represents exponential growth; if 0 < b < 1, it represents exponential decay.

Front

What is the significance of the constant 'a' in the exponential function y = a(b)^x?

Back

The constant 'a' determines the vertical stretch or compression of the graph.

Front

What transformation is represented by the equation y = 2^x + 4?

Back

This represents a vertical shift of 4 units upward.