Adding, Subtracting, Multiplying with Function Notation

Front

What is function notation?

Back

Function notation is a way to represent functions in mathematics, typically using symbols like f(x) to denote the output of a function f for a given input x.

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

How do you subtract one function from another, f(x) - g(x)?

Back

To subtract one function from another, you find the difference of their outputs: (f - g)(x) = f(x) - g(x).

Front

What is the product of two functions f(x) and g(x)?

Back

The product of two functions is found by multiplying their outputs: (f · g)(x) = f(x) * g(x).

Front

What is the result of f(x) = 2x + 1 and g(x) = 3x when added together?

Back

f(x) + g(x) = (2x + 1) + (3x) = 5x + 1.

Front

How do you find the difference between g(x) = x^2 - 1 and h(x) = 3x - 4?

Back

To find the difference, calculate g(x) - h(x) = (x^2 - 1) - (3x - 4) = x^2 - 3x + 3.

Front

What is the formula for multiplying two linear functions f(x) = ax + b and g(x) = cx + d?

Back

The product is given by (f · g)(x) = (ax + b)(cx + d) = acx^2 + (ad + bc)x + bd.

Front

What is the significance of the coefficients in a polynomial function?

Back

Coefficients determine the shape and position of the graph of the polynomial function, affecting its slope and intercepts.

Front

How do you evaluate a function at a specific value, say f(2) for f(x) = 3x - 5?

Back

To evaluate f(2), substitute 2 for x: f(2) = 3(2) - 5 = 6 - 5 = 1.

Front

What is the process for combining functions using function notation?

Back

Combining functions involves using operations like addition, subtraction, multiplication, or composition, expressed as (f + g)(x), (f - g)(x), (f · g)(x), or (f ∘ g)(x).