Key Features of Functions

Front

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

Back

The x-intercept is the point where the graph of the function 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 x-intercept of a function?

Back

To find the x-intercept, set y (or f(x)) to 0 and solve for x.

Front

How do you find the y-intercept of a function?

Back

To find the y-intercept, set x to 0 and solve for y (or f(0)).

Front

What does the notation f(x) represent?

Back

f(x) represents a function of x, indicating the output value of the function for a given input x.

Front

Evaluate f(x) = x - 5 at x = 0.

Back

f(0) = 0 - 5 = -5.

Front

What is the general form of a quadratic function?

Back

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

Front

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

Back

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

Front

How can you determine where a function is positive or negative?

Back

A function is positive where its output (f(x)) is greater than 0 and negative where its output is less than 0.

Front

What does it mean for a function to be increasing or decreasing?

Back

A function is increasing if f(x1) < f(x2) for x1 < x2, and decreasing if f(x1) > f(x2) for x1 < x2.

Front

What is the standard form of a linear function?

Back

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