Function Intercepts and Zeros

Front

What are the x- and y- intercepts of a function?

Back

The x-intercept is the point where the graph crosses the x-axis (y=0), and the y-intercept is where it crosses the y-axis (x=0).

Front

How do you find the y-intercept of the equation 3x + y = 5?

Back

Set x = 0. The equation becomes y = 5, so the y-intercept is (0, 5).

Front

What is an extremum in a function?

Back

An extremum is a point in the domain of a function where the function takes on a maximum or minimum value.

Front

What is the difference between absolute and relative extrema?

Back

Absolute extrema are the highest or lowest points over the entire domain, while relative extrema are the highest or lowest points in a specific interval.

Front

How can you determine the number of extrema in a graph?

Back

Count the peaks (maxima) and valleys (minima) in the graph.

Front

What does the range of a function represent?

Back

The range is the set of all possible output values (y-values) of a function.

Front

How do you determine the range of a quadratic function?

Back

Identify the vertex and the direction the parabola opens. For example, if it opens downwards and the vertex is the maximum point, the range is y ≤ vertex_y.

Front

What is a relative maximum?

Back

A relative maximum is a point where the function value is higher than the values of the function at nearby points.

Front

What is a relative minimum?

Back

A relative minimum is a point where the function value is lower than the values of the function at nearby points.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the highest or lowest point of the parabola, depending on its orientation.