Exponential Attributes and Transformations

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers, represented as -∞ < x < ∞.

Front

What does the y-intercept of a function represent?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented as (0, y).

Front

What is an asymptote in the context of exponential functions?

Back

An asymptote is a line that the graph approaches but never touches. For example, y = 0 is a horizontal asymptote for exponential decay.

Front

What transformation occurs when a function is reflected over the x-axis?

Back

When a function is reflected over the x-axis, all y-values are multiplied by -1.

Front

How does a vertical shift affect the graph of a function?

Back

A vertical shift moves the graph up or down. For example, g(x) = f(x) + k shifts the graph up by k units if k > 0 and down if k < 0.

Front

What does a horizontal shift do to the graph of a function?

Back

A horizontal shift moves the graph left or right. For example, g(x) = f(x - h) shifts the graph right by h units if h > 0 and left if h < 0.

Front

What is the effect of multiplying a function by a negative number?

Back

Multiplying a function by a negative number reflects the graph over the x-axis.

Front

What does the notation f(x) = a * b^x represent?

Back

This notation represents an exponential function where 'a' is a constant, 'b' is the base, and 'x' is the exponent.

Front

How do you find the y-intercept of an exponential function?

Back

To find the y-intercept, evaluate the function at x = 0.

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is f(x) = a * b^(x - h) + k, where (h, k) is the point of transformation.