Brooks Adv Alg_Pract_Final Exam Review PART 2

Front

What is the empirical rule in statistics?

Back

The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

Front

What percentage of a normal distribution lies between the mean and one standard deviation above the mean?

Back

34%.

Front

What is a logarithmic function?

Back

A logarithmic function is the inverse of an exponential function, expressed as y = log_b(x), where b is the base and x is the argument.

Front

What is the domain of the function g(x) = 3 log_3(x + 2)?

Back

The domain is x > -2, since the argument of the logarithm must be positive.

Front

What is the vertical asymptote of the function f(x) = -4x / (x^2 - 4x - 4)?

Back

To find the vertical asymptote, set the denominator equal to zero: x^2 - 4x - 4 = 0. The solutions are x = 2 ± √8.

Front

What does it mean for a function to have a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of the function approaches as x approaches positive or negative infinity.

Front

How do you solve the equation √(5x + 10) - 4 = 1?

Back

Add 4 to both sides to get √(5x + 10) = 5. Square both sides to get 5x + 10 = 25, leading to x = 3.

Front

What is the significance of the area under the curve in a normal distribution?

Back

The area under the curve represents the total probability, which is equal to 1 (or 100%).

Front

What is the formula for the standard deviation of a normal distribution?

Back

The standard deviation (σ) is a measure of the amount of variation or dispersion in a set of values.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) is associated with exactly one output (y-value).