IM-3: 1.3 Describing Graphs

Front

What is the interval of decrease for a function?

Back

The interval of decrease is the range of x-values where the function's output (y-value) is decreasing. For example, if a function decreases from negative infinity to 2, the interval of decrease is (-∞, 2).

Front

What are x-intercepts of a function?

Back

X-intercepts are the points where the graph of a function crosses the x-axis. At these points, the output (y-value) is zero. For example, the x-intercepts (-3,0), (-2,0), (2,0), and (3,0) indicate where the function equals zero.

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, if the range is [-2, ∞), it means the function can output any value from -2 to positive infinity.

Front

How do you determine the range of a quadratic function?

Back

To determine the range of a quadratic function, identify the vertex and the direction the parabola opens. For example, if the vertex is at (0, 4) and the parabola opens downwards, the range is y ≤ 4.

Front

What is an increasing interval in a function?

Back

An increasing interval is a range of x-values where the function's output (y-value) is increasing. For example, if a function increases from -1 to 1, the increasing interval is (-1, 1).

Front

Define a decreasing interval in a function.

Back

A decreasing interval is a range of x-values where the function's output (y-value) is decreasing. For example, if a function decreases from -∞ to 2, the decreasing interval is (-∞, 2).

Front

What is the significance of x-intercepts in graphing?

Back

X-intercepts are significant because they indicate where the function crosses the x-axis, helping to identify the roots of the equation and the behavior of the graph.

Front

How can you find the range of a function from its graph?

Back

To find the range from a graph, observe the lowest and highest points on the y-axis that the graph reaches. The range is then expressed in interval notation.

Front

What does it mean if a function has no x-intercepts?

Back

If a function has no x-intercepts, it means the graph does not cross the x-axis, indicating that the function does not have real roots.

Front

Explain the concept of a vertex in 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. It is crucial for determining the range.