Graphing Exponential and Logarithmic Functions

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is y = 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 horizontal asymptote of an exponential function?

Back

The horizontal asymptote of an exponential function of the form y = a(b)^x is typically y = 0.

Front

What is an asymptote in the context of graphing functions?

Back

An asymptote is a line that a graph approaches but never touches or crosses. It can be vertical, horizontal, or oblique.

Front

For the function f(x) = (1/2)^x, what is the domain?

Back

The domain of f(x) = (1/2)^x is all real numbers, or (-∞, ∞).

Front

For the function f(x) = (1/2)^x, what is the range?

Back

The range of f(x) = (1/2)^x is (0, ∞).

Front

What is the vertical asymptote of the function f(x) = 2(3)^x?

Back

The vertical asymptote of the function f(x) = 2(3)^x does not exist, as exponential functions do not have vertical asymptotes.

Front

How does the base of an exponential function affect its graph?

Back

If the base 'b' is greater than 1, the function increases; if 0 < b < 1, the function decreases.

Front

What is the significance of the constant 'a' in the exponential function y = a(b)^x?

Back

The constant 'a' represents the initial value or the y-intercept of the function when x = 0.

Front

What is the effect of changing the value of 'a' in the function y = a(b)^x?

Back

Changing the value of 'a' vertically stretches or compresses the graph and can also reflect it across the x-axis if 'a' is negative.

Front

What is the relationship between exponential functions and logarithmic functions?

Back

Exponential functions and logarithmic functions are inverses of each other. If y = b^x, then x = log_b(y).