Unit 4A Final Review & Retest Remediation

Front

What is the end behavior of a graph when x → ∞?

Back

The end behavior of a graph as x → ∞ can be described as y → ∞ or y → -∞ depending on the function. For example, if the graph rises indefinitely, then y → ∞.

Front

How do you determine the interval in which a function is decreasing?

Back

To determine the interval where a function is decreasing, look for sections of the graph where the y-values decrease as x-values increase. This can often be found by analyzing the derivative of the function.

Front

What is the significance of the x-intercept in a function's graph?

Back

The x-intercept indicates the points where the graph crosses the x-axis, which helps determine when an object hits the ground or when the function equals zero.

Front

What does it mean if a graph has a minimum value?

Back

A graph has a minimum value if there is a point on the graph that is lower than all other points in its vicinity, indicating the lowest point of the function.

Front

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

Back

A graph is positive on an interval if the y-values of the function are above the x-axis for all x-values in that interval.

Front

Define the term 'vertex' in the context of a quadratic function.

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

What is the difference between a maximum and a minimum value in a graph?

Back

A maximum value is the highest point on the graph, while a minimum value is the lowest point. A function can have either or both depending on its shape.

Front

How can you identify the y-intercept of a function?

Back

The y-intercept of a function is found by evaluating the function at x = 0, which gives the point where the graph crosses the y-axis.

Front

What does the interval notation (-∞, -3) represent?

Back

The interval notation (-∞, -3) represents all real numbers less than -3, indicating where the function is decreasing.

Front

Explain the concept of 'increasing' in a function's graph.

Back

A function is increasing on an interval if the y-values rise as the x-values increase, meaning the graph moves upwards from left to right.