Math 3 Unit 1-4 Test

Front

What is a hole in the graph of a function?

Back

A hole in the graph of a function occurs at a point where the function is not defined, typically due to a factor in the numerator and denominator that cancels out.

Front

How do you calculate the future value of an investment compounded continuously?

Back

The formula is A = Pe^(rt), where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate, and t is the time in years.

Front

What is an extraneous solution?

Back

An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.

Front

What is the relationship between a logarithmic function and its inverse?

Back

The logarithmic function and its inverse (exponential function) reflect over the line y=x on a graph.

Front

How do you find the ending balance of an investment compounded continuously?

Back

Use the formula A = Pe^(rt), substituting P for the initial investment, r for the interest rate, and t for the time in years.

Front

What is the formula for compound interest?

Back

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years.

Front

What does it mean for two functions to be perpendicular on a graph?

Back

Two functions are perpendicular if their slopes are negative reciprocals of each other.

Front

What is the significance of the line y=x in relation to functions?

Back

The line y=x is significant because it represents the points where the output of a function equals its input, and it is where a function and its inverse reflect.

Front

How do you check for extraneous solutions in an equation?

Back

To check for extraneous solutions, substitute the solution back into the original equation to see if it holds true.

Front

What is the continuous compounding formula used for?

Back

The continuous compounding formula is used to calculate the future value of an investment when interest is compounded continuously.