Key Features of Functions

Front

What are the zeros (x intercepts) of a function?

Back

The zeros (x intercepts) of a function are the values of x for which the function equals zero. For example, if a function f(x) has zeros at x = 0 and x = 4, then f(0) = 0 and f(4) = 0.

Front

What does it mean for a graph to be constant on an interval?

Back

A graph is constant on an interval if the function's value does not change for any x in that interval. For example, if a function is constant on the interval (-3, -1), it means that for all x values between -3 and -1, the function outputs the same value.

Front

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

Back

The y-intercept of a function is found by evaluating the function at x = 0. It is the point where the graph crosses the y-axis. For example, if f(0) = 3, then the y-intercept is (0, 3).

Front

What is the significance of the y-intercept in a graph?

Back

The y-intercept indicates the value of the function when x is zero. It provides a starting point for graphing the function and helps in understanding the function's behavior.

Front

What is a minimum point on a graph?

Back

A minimum point on a graph is the lowest point in a given interval. It represents the smallest value of the function. For example, if a function has a minimum at (-0.5, -3.5), then -3.5 is the lowest value of the function at x = -0.5.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x values) for which the function is defined. For example, the domain of f(x) = 1/x is all real numbers except x = 0.

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, the range of f(x) = x^2 is all non-negative real numbers.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, as x increases, the value of the function also increases. For example, if f(x) is increasing on (1, 3), then f(1) < f(2) < f(3).

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, as x increases, the value of the function decreases. For example, if f(x) is decreasing on (2, 4), then f(2) > f(3) > f(4).

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where a function approaches infinity or negative infinity as x approaches a. For example, the function f(x) = 1/(x-2) has a vertical asymptote at x = 2.