Traits of Exponential Function Part 2

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers, represented as (-∞, ∞).

Front

What is an asymptote in the context of exponential functions?

Back

An asymptote is a line that the graph of a function approaches but never touches. For exponential functions, this is often a horizontal line.

Front

What is the general form of an exponential function?

Back

The general form is f(x) = a * b^(x - h) + k, where (h, k) is the shift of the graph.

Front

What does the base 'b' in an exponential function represent?

Back

The base 'b' determines the rate of growth or decay. If b > 1, the function grows; if 0 < b < 1, it decays.

Front

How does changing the value of 'a' in the function f(x) = a * b^x affect the graph?

Back

Changing 'a' affects the vertical stretch or compression of the graph. If 'a' is positive, the graph opens upwards; if negative, it opens downwards.

Front

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

Back

The horizontal asymptote is y = -3.

Front

What is the vertical asymptote of the function f(x) = 1/(x + 2)?

Back

The vertical asymptote is x = -2.

Front

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

Back

The y-intercept can be found by evaluating the function at x = 0, which gives f(0) = a * b^0 = a.

Front

What is the effect of a negative exponent in an exponential function?

Back

A negative exponent indicates a decay, meaning the function approaches zero as x increases.

Front

What is the range of an exponential function?

Back

The range of an exponential function is all real numbers greater than the horizontal asymptote.