MTH 112: Analyzing Graphs of Functions

Use the graph of the function to find the ______ and range of f. (Enter your answers using interval notation.)

When using the Vertical Line Test, if any vertical line intersects the graph more than once, it is not a ______ of x.

To find the ______ of the function algebraically, set f(x) = 0 and solve for x.

To determine open intervals where a function is increasing, decreasing, or constant, analyze the ________ of the function.

When determining where a function is increasing, decreasing, or constant, the intervals should be expressed as open ______.

Use a graphing utility to graph the function and visually determine the open ______ on which the function is increasing, decreasing, or constant.

To verify results regarding increasing, decreasing, or constant intervals, create a ______ of values.

The ______ rate of change of the function from $x_1$ to $x_2$ is the slope of the secant line passing through the points $(x_1, f(x_1))$ and $(x_2, f(x_2))$.

To determine whether a function is even, odd, or neither, one must analyze its ______.

The graph of an even function is symmetric with respect to the ______.

Applying the Vertical Line Test to a graph is a visual technique used to determine if it represents $y$ as a ______ of $x$.

When a function is neither even nor odd, it possesses ______ symmetry.

A ______ function satisfies the condition $f(x) = f(-x)$ for all $x$ in its domain.

If $h(x) = x^2 - 1$, the result of $h(-x)$ will show if the function is even, odd, or ______.

Functions like $f(x) = 6x^{3/2}$ that exhibit no symmetry are classified as ______.

To analyze a function's intervals of increasing, decreasing, or being constant, the correct type of ______ must be used.

When visually examining a graph, areas where the $y$-values rise as $x$ increases indicate the function is ______.

A secant line is used to compute the ______ rate of change between two points on the graph.

For the function $f(x) = x^2 - 4x + 9$, understanding how to compute its average ______ of change helps analyze its behavior.

Symmetry about the y-axis is a key indicator of an ______ function.

The domain of a function is described using interval ______.

When a function's output does not increase or decrease over an interval, it is considered ______ on that interval.

Visually, the zeros of a function correspond to the points where the function's graph intersects the ______

Points such as relative minimums or maximums help summarize function traits and should be ______.