Key Feat. Sect1-3 & Transformations

Front

What is the behavior of a graph on the interval (e, ∞)?

Back

The graph is negative and decreasing.

Front

How do you determine the number of extrema (maxima and minima) in a graph?

Back

Count the number of peaks and valleys in the graph; in this case, there are 3 extrema.

Front

What is the end behavior of a function as x approaches negative infinity?

Back

As x approaches -∞, y approaches ∞.

Front

What does it mean for a graph to be positive on a given interval?

Back

The graph is above the x-axis on that interval; for example, it is positive on the domain (-∞, -5).

Front

What does the transformation f(-x+3)+4 represent?

Back

It represents a reflection over the y-axis, a shift left by 3 units, and a shift up by 4 units.

Front

What is the significance of the y-axis in graph transformations?

Back

The y-axis is the line of reflection for transformations involving negative inputs.

Front

How do you identify the maximum and minimum points on a graph?

Back

Maximum points are peaks where the graph changes from increasing to decreasing, and minimum points are valleys where it changes from decreasing to increasing.

Front

What does it mean for a function to be decreasing on an interval?

Back

The function's output values decrease as the input values increase within that interval.

Front

How can you determine the end behavior of a polynomial function?

Back

Analyze the leading term's degree and coefficient to predict the behavior as x approaches ±∞.

Front

What is the effect of shifting a graph left or right?

Back

Shifting left decreases the x-values, while shifting right increases the x-values of the graph.