Ch. 2 Functions and Their Graphs

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

How do you evaluate a function at a specific point?

Back

To evaluate a function at a specific point, substitute the value of the variable into the function's equation and simplify.

Front

What is the average rate of change of a function?

Back

The average rate of change of a function over an interval is the change in the function's value divided by the change in the input value over that interval.

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 range of the function f(x) = 2x^2 + 1?

Back

The range of f(x) = 2x^2 + 1 is [1, ∞) because the minimum value occurs at x=0, where f(0)=1.

Front

What is function composition?

Back

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

Front

How do you find g(f(x)) if f(x) = 2x and g(x) = 2x^2 - 1?

Back

To find g(f(x)), substitute f(x) into g: g(f(x)) = g(2x) = 2(2x)^2 - 1 = 8x^2 - 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

How do you determine the domain of the function f(x) = 2x^2 + 1?

Back

The domain of f(x) = 2x^2 + 1 is all real numbers, as there are no restrictions on x.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola.