Chapter 7 Test: Algebra

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What does the notation P(x) = 78,500(1.02)^x represent?

Back

This notation represents an exponential function where P(x) is the population at year x after 2000, starting with 78,500 and growing at a rate of 2% per year.

Front

How do you determine the growth rate from an exponential function?

Back

The growth rate can be found from the base of the exponential function. In P(x) = 78,500(1.02)^x, the growth rate is 2%.

Front

What is the difference between a linear function and an exponential function?

Back

A linear function has a constant rate of change, while an exponential function has a variable rate of change that increases or decreases multiplicatively.

Front

What does it mean to simplify an expression?

Back

Simplifying an expression means to reduce it to its simplest form by combining like terms and eliminating unnecessary parentheses.

Front

What is the Power over Root rule in exponents?

Back

The Power over Root rule states that when evaluating expressions with fractions as exponents, you should apply the exponent to the numerator and denominator separately.

Front

What is an example of a linear function?

Back

An example of a linear function is f(x) = 2x + 3, which represents a straight line when graphed.

Front

What is an example of an exponential function?

Back

An example of an exponential function is f(x) = 3(2)^x, which grows rapidly as x increases.

Front

What is the formula for calculating the slope of a line?

Back

The slope (m) of a line is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as the input values increase, the output values also increase.