Functions Review

Front

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

Back

The x-intercepts are the points where the graph of the function crosses the x-axis (y=0), and the y-intercept is the point where the graph crosses the y-axis (x=0).

Front

How do you calculate the average rate of change of a function between two points?

Back

The average rate of change from x=a to x=b is given by the formula: \( \frac{f(b) - f(a)}{b - a} \).

Front

Evaluate f(-2) if f(x) = x^2 + 3.

Back

f(-2) = (-2)^2 + 3 = 4 + 3 = 7.

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input from its domain.

Front

What does it mean for a relation to be 'not a function'?

Back

A relation is not a function if at least one input is associated with more than one output.

Front

How do you find the minimum value of a quadratic function?

Back

For a quadratic function in the form \( f(x) = ax^2 + bx + c \), the minimum value occurs at \( x = -\frac{b}{2a} \) if \( a > 0 \).

Front

What is the vertex of a parabola?

Back

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

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is \( f(x) = ax^2 + bx + c \), where a, b, and c are constants.

Front

How do you determine if a table of values represents a function?

Back

A table represents a function if each input (x-value) corresponds to exactly one output (y-value).

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant \( D = b^2 - 4ac \) determines the nature of the roots: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.