Front

What is a function in mathematics?

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 can you determine if a graph represents a function?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once (Vertical Line Test).

Front

What does it mean to evaluate a function at a specific point, such as f(33)?

Back

Evaluating a function at a specific point means substituting that point into the function's equation to find the corresponding output value.

Front

What is the significance of p(8)=52 in the context of Ms. Brackemyer's pencil collection?

Back

It means that after collecting pencils for 8 days, Ms. Brackemyer has a total of 52 pencils.

Front

How do you interpret the output of a function in a real-world context?

Back

The output of a function can represent a quantity or measurement that is relevant to the situation described by the function.

Front

What is the formula for the function g(x)=3x+4?

Back

This function calculates the total cost of x packages of bubble gum, where each package costs $3 and there is a fixed cost of $4.

Front

How do you find the value of g(8) in the context of the bubble gum problem?

Back

Substitute 8 into the function: g(8) = 3(8) + 4 = 28, meaning 8 packages of gum cost $28.

Front

What does it mean if a function is linear?

Back

A linear function is a function that graphs to a straight line, characterized by a constant rate of change.

Front

What is the general form of a linear function?

Back

The general form of a linear function is f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is the slope of a linear function?

Back

The slope of a linear function represents the rate of change of the function; it indicates how much the output value changes for a unit change in the input value.