Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions or formulas for different intervals of the input variable.

Front

How do you add two functions f(x) and g(x)?

Back

To add two functions, you combine their outputs: (f + g)(x) = f(x) + g(x).

Front

What is function composition?

Back

Function composition is the process of applying one function to the results of another function, denoted as (f ∘ g)(x) = f(g(x)).

Front

If f(x) = 2x and g(x) = x^2 + 3, what is f(g(2))?

Back

f(g(2)) = f(2^2 + 3) = f(7) = 2(7) = 14.

Front

What is the output of f(x) = 9 - 3x when x = 2?

Back

f(2) = 9 - 3(2) = 9 - 6 = 3.

Front

How do you find the value of a function at a specific point?

Back

To find the value of a function at a specific point, substitute the input value into the function's formula.

Front

What is the difference between f(x) and g(x) if f(x) = 5x and g(x) = 3x + 2?

Back

(f - g)(x) = f(x) - g(x) = 5x - (3x + 2) = 2x - 2.

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 valid output for that input, often due to division by zero or taking the square root of a negative number.

Front

If p(x) = 3x + 4, what is p(-2)?

Back

p(-2) = 3(-2) + 4 = -6 + 4 = -2.

Front

What is the result of f(x) + g(x) if f(x) = 4x and g(x) = 2x - 1?

Back

(f + g)(x) = f(x) + g(x) = 4x + (2x - 1) = 6x - 1.