U3LT 2 Review (Function Notation and Evaluating Functions)

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What is function notation?

Back

Function notation is a way to represent a function using symbols, typically in the form f(x), where f is the name of the function and x is the input variable.

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How can you represent the output of a function for a specific input?

Back

You can represent the output of a function for a specific input as an ordered pair (x, f(x)), where x is the input and f(x) is the output.

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What does it mean if f(a) = b?

Back

It means that when the input to the function f is a, the output is b.

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How do you evaluate a function at a specific value?

Back

To evaluate a function at a specific value, substitute the value into the function's expression and simplify.

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What is the sum of two functions?

Back

The sum of two functions f and g, denoted as (f + g)(x), is defined as f(x) + g(x) for all x in the domain of both functions.

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How do you find (g + f)(x)?

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To find (g + f)(x), you add the outputs of functions g and f for the same input x: (g + f)(x) = g(x) + f(x).

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What is function composition?

Back

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

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How do you evaluate a composition of functions, such as f(g(x))?

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To evaluate f(g(x)), first find g(x) and then substitute that result into the function f.

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What does h(t) = 5 mean in the context of a function representing height over time?

Back

It means that after t weeks, the height of the plant is 5 inches.

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What is the significance of the ordered pair (2, 4) in function notation?

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The ordered pair (2, 4) indicates that when the input is 2, the output of the function is 4.