Front

What is the definition of a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input from a given set.

Front

How do you evaluate a function at a specific point?

Back

To evaluate a function at a specific point, substitute the input value into the function's equation and simplify.

Front

What is the slope of a linear function?

Back

The slope of a linear function represents the rate of change of the function, calculated as the rise over run between two points on the line.

Front

How can you find the slope from a linear equation in standard form?

Back

To find the slope from a linear equation in standard form (Ax + By = C), rearrange it into slope-intercept form (y = mx + b) where m is the slope.

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, representing the output value when the input is zero.

Front

What does the term 'rate of change' refer to in a real-world context?

Back

The rate of change refers to how a quantity changes in relation to another quantity, often expressed as a slope in a linear model.

Front

How do you write a function to model a real-world situation?

Back

To write a function modeling a real-world situation, identify the quantities involved, determine how they relate, and express this relationship mathematically.

Front

What is a parent function?

Back

A parent function is the simplest form of a function type, from which more complex functions can be derived by transformations.

Front

How do transformations affect the graph of a function?

Back

Transformations such as translations, reflections, stretches, and compressions change the position and shape of the graph of a function.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.