You can evaluate a function using its graph, a table of values, or its equation. Evaluate the following functions for the given input values. Click “Submit” when finished.

Recall that we defined <EQUATION> to be the height of a ball <EQUATION> seconds after it is thrown into the air. There are only certain values of <EQUATION> and <EQUATION> that are possible in this situation. For example, it makes no sense to talk about the height of the ball when <EQUATION> or <EQUATION>. So, although <EQUATION> is a function of <EQUATION>, this function is only defined for certain values of <EQUATION>.

The set of inputs for which a function is defined is called the |b| domain |/b| of the function. The domain of the function in our example is the set of all real numbers between <EQUATION> and <EQUATION>.

Notice that <EQUATION>, the output value of the function, can only attain values between <EQUATION> and <EQUATION>. The set of output values of a function is called the |b| range |/b| of the function. The range of this function is the set of all real numbers between <EQUATION> and <EQUATION>.

Now let’s consider the function <EQUATION> whose graph is shown. We want to find the domain and range of this function. The domain of the function is the set of all possible input or <EQUATION>-values. By looking at the graph, you can see that that there is no restriction on the values of <EQUATION>. So the domain of this function is all real numbers. Now let’s find the range of this function.

The range of the function is the set of all possible output or \n<EQUATION>values. By looking at the graph, you can see that that the graph approaches the <EQUATION>axis, but does not touch it or pass below it. So the range of this function is all real numbers greater than zero.

Consider the graph of the function <EQUATION> . Find the domain and range of this function. Click “Submit” when finished.

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