12/123 Flashcard

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every x-value, there is one and only one corresponding y-value.

Front

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

Back

A relation is 'not a function' if at least one input is associated with more than one output. This violates the definition of a function.

Front

How do you solve the equation -11 + 3(b + 5) = 7?

Back

To solve for b, first distribute: -11 + 3b + 15 = 7. Combine like terms: 3b + 4 = 7. Then, subtract 4 from both sides: 3b = 3. Finally, divide by 3: b = 1.

Front

What is the solution to the equation 3(b - 4) = -3?

Back

To solve for b, first distribute: 3b - 12 = -3. Then, add 12 to both sides: 3b = 9. Finally, divide by 3: b = 3.

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of the steepness of the line, represented by 'm' in the equation f(x) = mx + b. It indicates how much y changes for a unit change in x.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented by 'b' in the equation f(x) = mx + b. It is the value of f(x) when x = 0.

Front

What is an example of a linear function?

Back

An example of a linear function is f(x) = 2x + 3, which has a slope of 2 and a y-intercept of 3.

Front

What is the difference between a function and a relation?

Back

A relation is any set of ordered pairs, while a function is a specific type of relation where each input is associated with exactly one output.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as the input (x) increases, the output (f(x)) also increases. This is indicated by a positive slope.