Alg 1 Desmos Unit 4 Describing Functions Review

Front

What is the minimum point of a function?

Back

The minimum point of a function is the point at which the function takes its lowest value. It is represented as a coordinate (x, y) where y is the minimum value.

Front

How do you calculate the average rate of change of a function over an interval?

Back

The average rate of change of a function f(x) over the interval [a, b] is calculated using the formula: \( \frac{f(b) - f(a)}{b - a} \).

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

How do you write the equation of a line given two points?

Back

To write the equation of a line given two points (x1, y1) and (x2, y2), first calculate the slope (m) using \( m = \frac{y2 - y1}{x2 - x1} \). Then use the point-slope form: \( y - y1 = m(x - x1) \).

Front

What does it mean for a function to be linear?

Back

A function is linear if it can be represented by a straight line on a graph, which means it has the form \( f(x) = mx + b \), where m is the slope and b is the y-intercept.

Front

What is a coordinate point?

Back

A coordinate point is a pair of numbers (x, y) that represent a specific location on a Cartesian plane.

Front

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

Back

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

Front

How do you determine if a point is a maximum or minimum on a graph?

Back

A point is a maximum if it is higher than all nearby points, and a minimum if it is lower than all nearby points. This can be visually assessed on a graph.

Front

What is the slope of a line?

Back

The slope of a line measures its steepness and direction, calculated as \( m = \frac{\text{rise}}{\text{run}} \), or the change in y over the change in x.

Front

What is a function?

Back

A function is a relation that assigns exactly one output (y) for each input (x). It can be represented as f(x).