PC 3.1-3.3 Flashcard

Front

What is the Range of the function in interval notation?

Back

The range is \( (0, \infty) \).

Front

What kind of transformation is represented by the function 2^x shifted right by 1 unit?

Back

The transformation is a right 1 unit shift.

Front

What type of function describes a situation where values increase rapidly?

Back

Exponential Growth.

Front

Back

The result is 2.

Front

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

Back

The horizontal asymptote is the line \( y = -4 \).

Front

Define 'exponential function'.

Back

An exponential function is a mathematical function of the form \( f(x) = a \cdot b^x \), where \( a \) is a constant, \( b \) is a positive real number, and \( b \neq 1 \).

Front

What is the general shape of an exponential growth graph?

Back

The graph rises steeply to the right and approaches the horizontal axis as it moves to the left.

Front

What does the base of an exponential function indicate?

Back

The base indicates the growth factor; if the base is greater than 1, the function represents growth.

Front

What is the significance of the y-intercept in an exponential function?

Back

The y-intercept represents the initial value of the function when \( x = 0 \).

Front

How do you find the horizontal asymptote of an exponential function?

Back

The horizontal asymptote can be found by analyzing the behavior of the function as \( x \) approaches infinity.