Exponential Functions Transformation [24-25]

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 a positive real number, and 'x' is the variable. The base 'b' determines the growth or decay rate.

Front

What is the parent function of exponential functions?

Back

The parent function of exponential functions is f(x) = b^x, where b > 0 and b ≠ 1.

Front

How does the graph of f(x) = b^x change when 'b' is greater than 1?

Back

When 'b' is greater than 1, the graph of f(x) = b^x increases rapidly as x increases, showing exponential growth.

Front

How does the graph of f(x) = b^x change when '0 < b < 1'?

Back

When '0 < b < 1', the graph of f(x) = b^x decreases rapidly as x increases, showing exponential decay.

Front

What effect does adding a constant to an exponential function have?

Back

Adding a constant 'k' to an exponential function f(x) = b^x results in a vertical shift of the graph. For example, f(x) = b^x + k shifts the graph 'k' units up.

Front

What does the transformation f(x) = b^(x-h) represent?

Back

The transformation f(x) = b^(x-h) represents a horizontal shift of the graph to the right by 'h' units.

Front

What does the transformation f(x) = b^(x) + k represent?

Back

The transformation f(x) = b^(x) + k represents a vertical shift of the graph upward by 'k' units.

Front

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

Back

A negative exponent in an exponential function, such as f(x) = b^(-x), reflects the graph across the y-axis, resulting in a decay function.

Front

How do you identify the vertical asymptote of an exponential function?

Back

The vertical asymptote of an exponential function f(x) = b^x + k is the line y = k, which the graph approaches but never touches.

Front

What is the significance of the base 'b' in an exponential function?

Back

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