IM algebra I Unit 5 Review

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. It shows rapid growth or decay.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base 'b' in f(x) = a(b^x) is greater than 1, leading to an increase in value. Exponential decay occurs when 'b' is between 0 and 1, leading to a decrease in value.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, represented by the equation f(x) = mx + b, where 'm' is the slope and 'b' is the y-intercept.

Front

How do you identify a linear function from an equation?

Back

A linear function can be identified by the presence of the variable 'x' raised only to the first power (e.g., f(x) = 2x + 3).

Front

What is the starting term in an exponential function?

Back

The starting term in an exponential function f(x) = a(b^x) is the constant 'a', which represents the value of the function when x = 0.

Front

How do you simplify the expression x^5 * x^7?

Back

To simplify x^5 * x^7, you add the exponents: x^(5+7) = x^12.

Front

What does the graph of an exponential growth function look like?

Back

The graph of an exponential growth function rises steeply to the right, showing rapid increases in value as x increases.

Front

What does the graph of an exponential decay function look like?

Back

The graph of an exponential decay function falls steeply to the right, showing rapid decreases in value as x increases.

Front

What is the general form of an exponential growth equation?

Back

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

Front

What is the general form of an exponential decay equation?

Back

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