District Test Units 9-12 Review #3

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, represented by a function of the form f(x) = a(1 + r)^x, where a is the initial amount and r is the growth rate.

Front

What does the base of an exponential function indicate?

Back

In an exponential function of the form f(x) = a(b)^x, the base b indicates the growth factor. If b > 1, the function represents exponential growth; if 0 < b < 1, it represents exponential decay.

Front

How do you identify exponential decay?

Back

Exponential decay is identified when the base of the exponential function is between 0 and 1 (0 < b < 1), indicating that the quantity decreases over time.

Front

What are the zeros of a function?

Back

The zeros of a function are the values of x for which f(x) = 0. They represent the points where the graph of the function intersects the x-axis.

Front

How do you factor by grouping?

Back

To factor by grouping, group terms with common factors, factor out the common factors, and then factor out the common binomial.

Front

What is the rate of increase in an exponential function?

Back

The rate of increase in an exponential function f(x) = a(b)^x is given by (b - 1) * 100%. For example, if b = 1.3, the rate of increase is (1.3 - 1) * 100% = 30%.

Front

What is the difference between linear growth and exponential growth?

Back

Linear growth increases by a constant amount over equal intervals, while exponential growth increases by a constant percentage, leading to faster growth over time.

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is f(x) = a(b)^x, where a is a constant, b is the base (growth factor), and x is the exponent.

Front

What does it mean if a function has a negative leading coefficient?

Back

If a function has a negative leading coefficient, it indicates that the graph of the function opens downwards, and the function will have a maximum point.

Front

How do you determine if a function is increasing or decreasing?

Back

A function is increasing if its derivative is positive over an interval, and it is decreasing if its derivative is negative over that interval.