Function Notation & Composite Functions Flashcard

Front

What is function notation?

Back

Function notation is a way to represent functions in mathematics, typically using symbols like f(x), g(x), etc., where 'f' or 'g' denotes the function and 'x' is the input variable.

Front

What is a composite function?

Back

A composite function is formed when one function is applied to the result of another function, denoted as (f∘g)(x) = f(g(x)).

Front

How do you find (g∘h)(x) if g(x)=3x+4 and h(x)=3x-1?

Back

To find (g∘h)(x), substitute h(x) into g: g(h(x)) = g(3x-1) = 3(3x-1) + 4 = 9x - 3 + 4 = 9x + 1.

Front

Evaluate g(25) if g(x)=6x-19.

Back

g(25) = 6(25) - 19 = 150 - 19 = 131.

Front

Evaluate f(12) if f(x)=\frac{3}{2}x+5.

Back

f(12) = \frac{3}{2}(12) + 5 = 18 + 5 = 23.

Front

If f(x) = -4x - 5 and g(x) = 3 - x, what is g(-4) + f(1)?

Back

g(-4) = 3 - (-4) = 7; f(1) = -4(1) - 5 = -9; g(-4) + f(1) = 7 - 9 = -2.

Front

Evaluate g(-12) if g(x) = \frac{3}{4}x + 10.

Back

g(-12) = \frac{3}{4}(-12) + 10 = -9 + 10 = 1.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What does it mean for a function to be linear?

Back

A function is linear if it can be represented by a straight line on a graph, typically in the form f(x) = mx + b, where m is the slope and b is the y-intercept.