AA~ HW ck 3-5 day 1

Front

What is the composition of functions f(g(x))?

Back

The composition of functions f(g(x)) means applying the function g to x first, and then applying the function f to the result of g.

Front

How do you determine if a relation is a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value). If any input is associated with more than one output, it is not a function.

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

How do you find the domain and range from a set of ordered pairs?

Back

To find the domain, list all the unique x-values from the ordered pairs. To find the range, list all the unique y-values.

Front

What does it mean for a graph to have a range of (1, ∞)?

Back

A range of (1, ∞) means that the output values (y-values) of the function are greater than 1 and extend to infinity.

Front

What is the significance of the vertical line test in determining functions?

Back

The vertical line test states that if a vertical line intersects a graph at more than one point, the graph does not represent a function.

Front

What is the value of f(g(3)) if f(x) = 2x - 1 and g(x) = x^2 - 4?

Back

To find f(g(3)), first calculate g(3) = 3^2 - 4 = 5. Then, calculate f(5) = 2(5) - 1 = 9.

Front

What is an example of a function that is not a function?

Back

An example of a relation that is not a function is {(1, 2), (1, 3)}, where the input 1 has two different outputs.

Front

How do you express the domain and range of the function {(0,1), (1,-3), (2,-4), (-4,1)}?

Back

Domain: D = {-4, 0, 1, 2}; Range: R = {-4, -3, 1}.