2024 Fall Final Exam Review 3

Front

What is an asymptote in the context of graphing functions?

Back

An asymptote is a line that a graph approaches but never touches. It can be vertical, horizontal, or oblique.

Front

Back

To solve the inequality, isolate x by simplifying both sides and then graph the solution on a number line.

Front

What does it mean for a graph to be shifted vertically?

Back

Front

How does changing the slope of a linear function affect its graph?

Back

Changing the slope alters the steepness of the line. A larger slope means a steeper line, while a smaller slope means a flatter line.

Front

Back

Multiplying a function by a constant compresses or stretches the graph vertically. In this case, the graph of g is compressed to one-fourth the height of f.

Front

What is the general form of a linear equation?

Back

Front

What does it mean for a function to be linear?

Back

A linear function is a function that graphs to a straight line, characterized by a constant rate of change (slope).

Front

How do you find the new equation of a line after transformations?

Back

To find the new equation, apply the transformations to the original slope and y-intercept. For example, doubling the slope and shifting down affects the equation accordingly.

Front

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

Back

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

Front

What is the relationship between two functions when one is a transformation of the other?

Back

Transformations can include shifts, stretches, or compressions, which change the position or shape of the graph without altering its fundamental properties.