Exponential functions 1/24/24

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is \( (-\infty, \infty) \).

Front

What is always the y-intercept of a basic exponential function?

Back

The y-intercept of a basic exponential function is (0,1).

Front

What is the y-intercept in the function \( y=4(2)^{x} \)?

Back

The y-intercept is (0,4).

Front

What is the equation of the horizontal asymptote for an exponential function?

Back

The horizontal asymptote is typically \( y = 0 \) for basic exponential functions, but can vary based on transformations.

Front

Is the function \( y=4(0.5)^{x} \) exponential growth or decay?

Back

It is exponential decay.

Front

What is the general form of an exponential function?

Back

The general form is \( y = ab^{x} \), where \( a \) is a constant and \( b \) is the base.

Front

What does the base \( b \) represent in an exponential function?

Back

The base \( b \) determines the rate of growth (if \( b > 1 \)) or decay (if \( 0 < b < 1 \)).

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 effect of a negative exponent in an exponential function?

Back

A negative exponent indicates a reciprocal, leading to decay.

Front

What is the range of a basic exponential function?

Back

The range of a basic exponential function is \( (0, \infty) \).