benchmark review2

Front

What is the composition of functions?

Back

The composition of functions is a way to combine two functions where the output of one function becomes the input of another. It is denoted as g(f(x)).

Front

Given f(x) = 2x - 8 and g(x) = 4x, what is g(f(x))?

Back

g(f(x)) = g(2x - 8) = 4(2x - 8) = 8x - 32.

Front

What does P(Male | Full-time) represent in probability?

Back

P(Male | Full-time) represents the probability of a student being male given that they are a full-time student.

Front

How do you find conditional probability?

Back

Conditional probability is found using the formula P(A | B) = P(A and B) / P(B), where A and B are events.

Front

What is the significance of the function g(x) = (x - 1)^3?

Back

This function represents a transformation of the original function f(x) = x^3, specifically a horizontal shift to the right by 1 unit.

Front

How do you evaluate f(h(5)) using function graphs?

Back

To evaluate f(h(5)), first find the value of h(5) from the graph, then use that value as the input for f(x) to find f(h(5)).

Front

Back

Front

What is the cube root of a number?

Back

The cube root of a number x is a value y such that y^3 = x.

Front

What is the difference between a function and its inverse?

Back

A function takes an input and produces an output, while its inverse takes the output and returns to the original input.

Front

What does the notation g(x) = x^3 + 1 indicate?

Back

This indicates a transformation of the cubic function f(x) = x^3, specifically a vertical shift upwards by 1 unit.