Flashcard- Function Operations

Front

What is function composition?

Back

Function composition is the process of applying one function to the results of another function. If you have two functions, f(x) and g(x), the composition is denoted as f(g(x)).

Front

What does it mean if a function is undefined at a certain point?

Back

A function is undefined at a certain point if there is no output for that input, often due to division by zero or taking the square root of a negative number.

Front

Calculate h(f(-2)) if f(-2) = 10 and h(x) = x - 10.

Back

h(f(-2)) = h(10) = 10 - 10 = 0.

Front

What is the distance Bill runs if he goes to Andy's house and back?

Back

Bill runs a total distance of 800 meters (400 meters to Andy's house and 400 meters back home).

Front

Given f(x) = 4x - 10 and g(x) = 2, find \frac{f}{g}(x).

Back

\frac{f}{g}(x) = \frac{4x - 10}{2} = 2x - 5.

Front

What is the output of f(g(3)) if g(3) = 2 and f(x) = 2x?

Back

f(g(3)) = f(2) = 2 * 2 = 4.

Front

Define the term 'domain' in relation to functions.

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

Define the term 'range' in relation to functions.

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What is the difference between distance and displacement?

Back

Distance is the total path length traveled, while displacement is the straight-line distance from the starting point to the endpoint, considering direction.

Front

If f(x) = x^2 and g(x) = x + 1, what is f(g(2))?

Back

g(2) = 2 + 1 = 3, so f(g(2)) = f(3) = 3^2 = 9.