Comparing Functions and Graphs (IM Unit 4 Lesson 9)

Front

What is the definition of a function in mathematics?

Back

A function is a relation that assigns exactly one output value for each input value.

Front

What does it mean for two functions to be equal at a certain point?

Back

Two functions f(x) and g(x) are equal at a point x if f(x) = g(x).

Front

How do you determine which function value is greater for a given input?

Back

To determine which function value is greater, evaluate both functions at the given input and compare the results.

Front

What is the significance of the notation f(x) in a function?

Back

f(x) represents the output of the function f for the input x.

Front

What does the inequality f(x) < g(x) indicate about the functions f and g?

Back

The inequality f(x) < g(x) indicates that the output of function f is less than the output of function g for the input x.

Front

How can you find the x-value where f(x) = g(x)?

Back

To find the x-value where f(x) = g(x), set the two functions equal to each other and solve for x.

Front

What is the graphical representation of a function?

Back

The graphical representation of a function is a plot of its input-output pairs on a coordinate plane.

Front

What does it mean if two functions intersect on a graph?

Back

If two functions intersect on a graph, it means they have the same output value for at least one input value.

Front

What is the importance of evaluating functions at specific points?

Back

Evaluating functions at specific points helps to compare their values and understand their behavior at those points.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input is associated with exactly one output.