LT 14 Operations of functions

Front

What is the sum of two functions g(n) = 4n - 4 and f(n) = 5n + 4?

Back

(g + f)(n) = 9n.

Front

What is the product of two functions g(x) = 2x + 2 and f(x) = 3?

Back

(g * f)(x) = 6x + 6.

Front

If f(x) = 2x - 4 and g(x) = x + 11, what is 3f(x) - g(x)?

Back

3f(x) - g(x) = 5x - 23.

Front

What is the difference between g(n) = 4n - 4 and f(n) = 5n + 4?

Back

(g - f)(n) = -n - 8.

Front

When f(x) = 9 - 3x and g(x) = 5x - 7, what is (f + g)(x)?

Back

(f + g)(x) = 2x + 2.

Front

Define the operation of function addition.

Back

Function addition combines two functions by adding their outputs for the same input: (f + g)(x) = f(x) + g(x).

Front

Define the operation of function subtraction.

Back

Function subtraction combines two functions by subtracting the output of one from the other for the same input: (f - g)(x) = f(x) - g(x).

Front

Define the operation of function multiplication.

Back

Function multiplication combines two functions by multiplying their outputs for the same input: (f * g)(x) = f(x) * g(x).

Front

What is the general form of a linear function?

Back

A linear function can be expressed as f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

The slope represents the rate of change of the function; it indicates how much y changes for a unit change in x.