Evaluating Functions

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What does it mean to evaluate a function?

Back

Evaluating a function means substituting a specific value for the variable in the function's expression to find the corresponding output.

Front

How do you find the value of f(x) for a given x?

Back

To find f(x), substitute the value of x into the function's equation and simplify.

Front

What is the sum of two functions?

Back

The sum of two functions f and g, denoted (f + g)(x), is found by adding their outputs: (f + g)(x) = f(x) + g(x).

Front

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

Back

f(4) = 2(4) + 3 = 8 + 3 = 11.

Front

What is the difference of two functions?

Back

The difference of two functions f and g, denoted (f - g)(x), is found by subtracting their outputs: (f - g)(x) = f(x) - g(x).

Front

If f(x) = x^2 - 1, what is f(0)?

Back

f(0) = 0^2 - 1 = -1.

Front

What is the product of two functions?

Back

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

Front

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

Back

(f * g)(2) = f(2) * g(2) = (3*2) * (2 + 2) = 6 * 4 = 24.

Front

What is the quotient of two functions?

Back

The quotient of two functions f and g, denoted (f / g)(x), is found by dividing their outputs: (f / g)(x) = f(x) / g(x), provided g(x) ≠ 0.