2024 Fall Final Exam Review 3

Front

What is a transformation in the context of functions?

Back

A transformation refers to the alteration of a function's graph through shifts, stretches, compressions, or reflections.

Front

What does it mean for a function to be vertically compressed?

Back

A function is vertically compressed when its output values are multiplied by a factor between 0 and 1, making the graph closer to the x-axis.

Front

What is the definition of an asymptote?

Back

An asymptote is a line that a graph approaches but never touches or crosses.

Front

How does adding a constant to a function affect its graph?

Back

Adding a constant to a function shifts the graph vertically. If the constant is positive, the graph shifts up; if negative, it shifts down.

Front

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

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of the function; it indicates how much y changes for a unit change in x.

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

How do you determine the slope from two points on a line?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1) for points (x1, y1) and (x2, y2).

Front

What is the relationship between the graphs of f(x) and g(x) if g(x) = f(x) + k?

Back

The graph of g(x) is the graph of f(x) shifted vertically by k units. If k is positive, it shifts up; if negative, it shifts down.

Front

What does it mean for a function to have a negative slope?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant of the graph.