Multiple Representations

Front

What is a function in mathematics?

Back

A function is a relationship between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x is 0.

Front

How do you determine the rate of change (slope) in a linear function?

Back

The rate of change (slope) is calculated by taking the difference in the y-values divided by the difference in the x-values between two points on the line.

Front

What is the equation of a line in slope-intercept form?

Back

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

If a pizza costs $12 and each topping costs $1.99, how would you express the total cost as a function of the number of toppings?

Back

The total cost can be expressed as y = 1.99x + 12, where x is the number of toppings.

Front

What is the meaning of the slope in a real-world context?

Back

The slope represents the rate of change or how much one quantity changes in relation to another quantity.

Front

How do you find the y-intercept from a linear equation?

Back

To find the y-intercept, set x to 0 in the equation and solve for y.

Front

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

Back

The x-value represents the input of the function, which is used to determine the corresponding output (y-value).

Front

What does it mean if a function is linear?

Back

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

Front

How can you represent a real-world situation with a linear equation?

Back

You can represent a real-world situation with a linear equation by identifying the variables involved and determining how they relate to each other.