Use the graph of the function to find the domain and range...

Use the graph of the function to find the domain and range of $f$ and the indicated function values.
$$\begin{array}{ll}{\text { (a) } f(-2)} & {\text { (b) } f(1)} \\ {\text { (c) } f(0)} & {\text { (d) } f(2)}\end{array}$$

Key Concepts

Graph of a Function

A graph of a function is a visual representation that shows the relationship between the input values (typically on the horizontal axis) and the output values (typically on the vertical axis). It is used to understand the behavior of the function, including its trends, continuity, and any apparent restrictions on inputs or outputs.

Domain

The domain of a function is the complete set of possible input values (usually x-values) for which the function is defined. Determining the domain from a graph involves identifying the interval or set of x-values where the graph exists without any breaks or omissions.

Range

The range of a function is the set of all possible output values (usually y-values) that the function can produce. When using a graph, determining the range involves observing the vertical spread of the graph and noting the minimum and maximum values, if they exist.

Function Evaluation

Function evaluation involves substituting specific input values into the function to obtain the corresponding output. From a graph, this means locating the point with the given x-coordinate and reading off the corresponding y-value, which gives the function's value at that input.

Transcript

00:01 We're given the graph of a function, and we're asked to find the domain and range of this function.

00:08 And in each part, we're asked to find a given function value.

00:19 So the function is located in exercise 10 of this section.

00:24 We see its graph there.

00:27 Now, to find the domain of this function, you want to find all the xes, such that there is a y, such that the point xy, lies in the graph.

00:43 We see that given any x on the x axis, if we draw a vertical line through this point, we will intersect the graph at exactly one point.

00:53 And therefore, it follows that every x is in the domain, and the domain of our function, f, is the open interval in negative infinity, positive infinity, or the set of all real numbers are.

01:12 To find the range of our function, we want to find the set of all 1.

01:17 Y such that there is an x such that the point xy lies in the graph now we see that clearly if y is less than or equal to one we draw a horizontal line through that point on the y axis we will intersect the graph at at least one point and therefore all of these points lie in the range of so the range of y includes at least all y less than or equal to one.

01:53 What about y greater than one? well, if you draw a horizontal line through any of these points greater than one on the y -axis, see that we don't intersect the graph anywhere, and therefore these points do not line the range.

02:07 So the range of our function f, this is the interval negative infinity of 2 -1, close, bracket.

02:29 Now in part a we're asked to find the value f of negative 2.

02:38 Well, we look for negative 2 on our x -axis.

02:41 We draw a vertical line through it...

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