Flashcard - Graphing inverses and exponential functions

Front

What is the inverse of a function?

Back

The inverse of a function f(x) is a function f^-1(x) that reverses the effect of f(x). If f(a) = b, then f^-1(b) = a.

Front

If f(x) passes through (1, 4), what point does f^-1(x) pass through?

Back

(4, 1) because the coordinates are swapped in the inverse function.

Front

What is the general form of an exponential function?

Back

The general form is f(x) = a * b^x, where a is a constant and b is the base.

Front

What is the horizontal asymptote of the function f(x) = (1/2)^x?

Back

The horizontal asymptote is y = 0.

Front

What is the domain of the function f(x) = 2^x?

Back

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

Front

What is the range of the function f(x) = (1/2)^x?

Back

The range is (0, ∞).

Front

What does it mean for two functions to be inverses?

Back

Two functions f(x) and g(x) are inverses if f(g(x)) = x and g(f(x)) = x for all x in the domain.

Front

What is the inverse of g(x)?

Back

The inverse is denoted as g^-1(x).

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse, replace f(x) with y, swap x and y, and solve for y.

Front

What is the equation of the exponential function that passes through the point (0, 1)?

Back

The equation is f(x) = a * b^x where a = 1.