Unit 2B Test Review

Front

What is the inverse of a function?

Back

The inverse of a function f(x) is a function that reverses the effect of f. If f(x) = y, then the inverse function f⁻¹(y) = x.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse, swap the x and y in the equation and solve for y.

Front

What is the Richter scale?

Back

The Richter scale is a logarithmic scale used to measure the intensity of earthquakes based on the amplitude of seismic waves.

Front

What is the formula for calculating the Richter scale?

Back

R = log10(a) - log10(T) + B, where a is amplitude, T is time, and B is a constant.

Front

If the amplitude is 200 microns and the period is 1.7 seconds, what is the intensity of the earthquake if B = 3?

Back

The intensity is 5.1 on the Richter scale.

Front

What does it mean for two functions to be inverses based on their tables of values?

Back

Two functions are inverses if the inputs and outputs are switched; for every (x, y) in f, there is a (y, x) in g.

Front

What is the graphical representation of an inverse function?

Back

The graph of an inverse function is a reflection of the original function across the line y = x.

Front

How can you determine if two functions are inverses using their graphs?

Back

If the graphs of the two functions are symmetric with respect to the line y = x, they are inverses.

Front

What is the significance of the constant B in the Richter scale formula?

Back

The constant B adjusts the scale to account for different reference conditions in measuring seismic waves.

Front

What is the relationship between amplitude and intensity on the Richter scale?

Back

Higher amplitude values lead to higher intensity readings on the Richter scale.