Family of Functions Review

Front

What is a family of functions?

Back

A family of functions is a group of functions that share common characteristics, such as the same general form or behavior.

Front

What is the vertex of a parabola?

Back

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

Front

How do you find the vertex of a quadratic function in vertex form?

Back

For a quadratic function in the form f(x) = a(x - h)² + k, the vertex is the point (h, k).

Front

What does the 'a' value in a quadratic function indicate?

Back

The 'a' value determines the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.

Front

How can you determine if a quadratic function opens up or down?

Back

You can determine this by looking at the 'a' value in the function: if 'a' is positive, it opens up; if 'a' is negative, it opens down.

Front

What is the absolute value function?

Back

The absolute value function is defined as f(x) = |x|, which outputs the non-negative value of x.

Front

What is the general form of a linear function?

Back

The general form of a linear function is f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Front

What is the y-intercept of a function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented as (0, b) in the equation f(x) = mx + b.