6.4 Graphing Exponential Functions

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 the general shape of the graph of an exponential function?

Back

The graph of an exponential function increases rapidly (for b > 1) or decreases rapidly (for 0 < b < 1) as x increases, and approaches the x-axis but never touches it.

Front

What does the base of an exponential function determine?

Back

The base determines the rate of growth or decay of the function. If the base is greater than 1, the function grows; if the base is between 0 and 1, the function decays.

Front

What is the y-intercept of the function y=2^x?

Back

The y-intercept is (0, 1) because when x=0, y=2^0=1.

Front

What is the domain of the function y=2^x?

Back

The domain is all real numbers, (-∞, ∞).

Front

What is the range of the function y=2^x?

Back

The range is y > 0, meaning the function only takes positive values.

Front

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

Back

To find the y-intercept, substitute x=0 into the function and solve for y.

Front

What is the equation of the exponential function that passes through the point (0, 3)?

Back

The equation is y=3^x.

Front

What happens to the graph of y=2^x as x approaches negative infinity?

Back

As x approaches negative infinity, y approaches 0, meaning the graph gets closer to the x-axis.

Front

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

Back

Changing the base affects the steepness of the graph. A larger base results in a steeper curve.