Module 6 Day 1 Guided

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

What is the definition of a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane as a straight line, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

Which of the following is NOT a linear function: y = 2x + 3 or y = x^2?

Back

y = x^2 is NOT a linear function; it is a quadratic function.

Front

How can 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 x-value is associated with more than one y-value, it is not a function.

Front

What does it mean for a relation to be 'not a function'?

Back

A relation is 'not a function' if there exists at least one input that corresponds to multiple outputs.

Front

What is the vertical line test?

Back

The vertical line test is a method used to determine if a curve is a function. If any vertical line intersects the curve more than once, the curve is not a function.

Front

What is an example of a function?

Back

An example of a function is f(x) = 3x + 2, where each input x produces a unique output.

Front

What is an example of a relation 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 corresponds to two different outputs.

Front

What is the significance of the x-values in a function?

Back

The x-values (or inputs) in a function are significant because they determine the corresponding y-values (or outputs). Each x-value must map to only one y-value.

Front

What does it mean for x-values to repeat in a table of values?

Back

If x-values repeat in a table of values, it indicates that the relation is not a function, as it suggests that a single input is associated with multiple outputs.