Transformations of Exponential Equations

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is the base (a positive real number), and x is the exponent.

Front

What does a vertical translation of an exponential function mean?

Back

A vertical translation shifts the graph of the function up or down. For example, f(x) = b^x + k shifts the graph up by k units if k > 0 and down by k units if k < 0.

Front

What does a horizontal translation of an exponential function mean?

Back

A horizontal translation shifts the graph of the function left or right. For example, f(x) = b^(x - h) shifts the graph right by h units if h > 0 and left by h units if h < 0.

Front

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

Back

It translates the graph of g(x) = 3^x down by 4 units.

Front

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

Back

Adding a positive constant shifts the graph vertically upwards.

Front

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

Back

Subtracting a positive constant shifts the graph vertically downwards.

Front

What transformation occurs in the function f(x) = 2^(x + 3)?

Back

This function shifts the graph of the basic function 2^x left by 3 units.

Front

What transformation occurs in the function f(x) = 2^(x - 3)?

Back

This function shifts the graph of the basic function 2^x right by 3 units.

Front

If f(x) = 2^x + 5, what is the vertical transformation?

Back

The graph is shifted up by 5 units.

Front

If f(x) = 2^x - 2, what is the vertical transformation?

Back

The graph is shifted down by 2 units.