Exponential Function Transformations

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 is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

Front

Determine the horizontal asymptote for the function f(x) = 3(2)^(x-4) + 5.

Back

y = 5.

Front

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

Back

Reflecting a function over the x-axis means to invert the output values, changing f(x) to -f(x).

Front

If y = -2^(x - 3), what is the transformation from its parent function?

Back

Reflected about the x-axis and translated right 3.

Front

What is the range of the function f(x) = 2^x?

Back

The range is y > 0.

Front

What does it mean to translate a function?

Back

Translating a function means shifting its graph horizontally and/or vertically without changing its shape.

Front

Use the graph of y = 2^(x+1) - 3. What is the transformation from the parent function y = 2^x?

Back

Translated left 1 and down 3.

Front

What is the parent function of exponential functions?

Back

The parent function of exponential functions is f(x) = b^x, where b > 0.

Front

How do you write a function that is reflected over the line x=0?

Back

To reflect a function over the line x=0, replace x with -x in the function.