Exponential and Logarithmic Functions

Front

What is the vertical asymptote of the function f(x)=log_5(x+4) - 2?

Back

The vertical asymptote is x = -4.

Front

What is the general form of an exponential growth function?

Back

The general form of an exponential growth function is f(x) = a * b^x, where a > 0 and b > 1.

Front

What is the general form of an exponential decay function?

Back

The general form of an exponential decay function is f(x) = a * b^x, where a > 0 and 0 < b < 1.

Front

How do you identify if a graph represents exponential growth or decay?

Back

If the graph rises as x increases, it represents exponential growth. If it falls as x increases, it represents exponential decay.

Front

What transformation does the function f(x)=log_5(x+4) - 2 undergo?

Back

The function undergoes a translation 4 units to the left and 2 units down.

Front

What is the base of the logarithm in the function f(x)=log_5(x+4) - 2?

Back

The base of the logarithm is 5.

Front

What does the term 'asymptote' refer to in the context of logarithmic functions?

Back

An asymptote is a line that a graph approaches but never touches. For logarithmic functions, it is typically a vertical line.

Front

What is the effect of adding a constant to a logarithmic function, such as in f(x)=log_5(x+4) - 2?

Back

Adding a constant shifts the graph vertically. In this case, it shifts the graph down by 2 units.

Front

What is the significance of the point where the graph of an exponential function crosses the y-axis?

Back

The point where the graph crosses the y-axis represents the initial value of the function, which is f(0) = a.

Front

How can you determine the y-intercept of an exponential function in the form f(x) = a * b^x?

Back

The y-intercept can be found by evaluating f(0), which gives f(0) = a.