O4C1 Non-Linear Functions (Exponential Functions)

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 exponent.

Front

What is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function is the value of the function when x = 0, which is equal to the constant 'a' in the function f(x) = a * b^x.

Front

What does it mean for a function to exhibit growth?

Back

A function exhibits growth if its value increases as the input (x) increases. In exponential functions, this occurs when the base 'b' is greater than 1.

Front

What does it mean for a function to exhibit decay?

Back

A function exhibits decay if its value decreases as the input (x) increases. In exponential functions, this occurs when the base 'b' is between 0 and 1.

Front

How can you determine if a function is linear or exponential?

Back

A function is linear if it can be expressed in the form y = mx + b, where m and b are constants. It is exponential if it can be expressed in the form y = a * b^x.

Front

What is the general shape of the graph of an exponential growth function?

Back

The graph of an exponential growth function rises steeply to the right and approaches the x-axis but never touches it.

Front

What is the general shape of the graph of an exponential decay function?

Back

The graph of an exponential decay function starts high on the left and decreases towards the x-axis, approaching it but never touching it.

Front

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

Back

The base 'b' in an exponential function represents the growth (if b > 1) or decay (if 0 < b < 1) factor of the function.

Front

What is the significance of the y-intercept in real-world applications of exponential functions?

Back

The y-intercept often represents the initial value or starting amount in real-world scenarios, such as population, investment, or material quantity.

Front

How do you identify exponential growth from a table of values?

Back

Exponential growth can be identified in a table of values by observing that the ratio of consecutive outputs (y-values) remains constant.