[2] Fall Final Review 2024

Front

What is the x-intercept of a function?

Back

The x-intercept is the point where the graph of a function crosses the x-axis. It is represented as a coordinate (x, 0). For example, the x-intercept of the function is (-3, 0).

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. For example, the correct domain for the function is -2 ≤ x ≤ 2.

Front

How do you solve the equation -6x - 20 = -2x + 4(1 - 3x)?

Back

To solve for x, first simplify the equation: -6x - 20 = -2x + 4 - 12x. Combine like terms to get -6x + 12x = 4 + 20, which simplifies to 3x = 24. Thus, x = 3.

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. For example, the correct range for the function is 0 ≤ y < 3.5.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect. For example, a line passing through (6, 2) and parallel to the equation y = \frac{1}{2}x - 12 has the same slope of \frac{1}{2}.

Front

How do you find the slope of a line given two points?

Back

The slope (m) of a line through two points (x1, y1) and (x2, y2) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the slope-intercept form of a linear equation?

Back

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

Front

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

Back

The y-intercept is the point where the graph of the equation crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

How do you determine if a function is increasing or decreasing?

Back

A function is increasing if its slope is positive (the graph rises as you move from left to right) and decreasing if its slope is negative (the graph falls as you move from left to right).

Front

What is the difference between open and closed intervals?

Back

An open interval (a, b) does not include the endpoints a and b, while a closed interval [a, b] includes both endpoints.