Pre-Calculus P5 HW 01.06.25: graphs of Exponential Functions

Front

What is an exponential function?

Back

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

Front

What does the graph of an exponential growth function look like?

Back

The graph of an exponential growth function rises rapidly as x increases, starting from a point above the x-axis and approaching zero as x decreases.

Front

What does the graph of an exponential decay function look like?

Back

The graph of an exponential decay function decreases rapidly as x increases, starting from a point above the x-axis and approaching zero as x increases.

Front

What is the base of an exponential function?

Back

The base of an exponential function is the constant 'b' in the function y = a * b^x, which determines the rate of growth or decay.

Front

How do you identify exponential growth vs. decay from an equation?

Back

If the base 'b' is greater than 1, the function represents exponential growth. If 'b' is between 0 and 1, it represents exponential decay.

Front

What is the effect of changing the exponent in an exponential function?

Back

Changing the exponent affects the steepness and direction of the graph. A positive exponent results in growth, while a negative exponent results in decay.

Front

What does the equation y = 2^x represent?

Back

The equation y = 2^x represents an exponential growth function where the base is 2, indicating that the function doubles for every increase of 1 in x.

Front

What does the equation y = 2^-x represent?

Back

The equation y = 2^-x represents an exponential decay function where the base is 2, indicating that the function halves for every increase of 1 in x.

Front

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

Back

The y-intercept of an exponential function is the value of y when x = 0, which is equal to 'a' in the function y = a * b^x.

Front

How does the transformation y = 2^(x+3) affect the graph of y = 2^x?

Back

The transformation y = 2^(x+3) shifts the graph of y = 2^x to the left by 3 units.