Question

Math

Posted 4 months ago

```
(10 pts) 3. The graph of $y=f(x)$ is shown below.
(a) Determine the domain and the range of the function $f$, in interval notation.
Domain: $\qquad$
Range: $\qquad$
```

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Answer from Sia

Verified answer

Posted 4 months ago

Solution by Steps

step 1

To determine the domain of the function $f(x)$, we need to identify the set of all $x$-values for which the function is defined. From the graph, we observe that the function starts at $x = -4$ and ends at $x = 6$

step 2

Therefore, the domain of $f(x)$ is the interval $[-4, 6]$

step 3

To determine the range of the function $f(x)$, we need to identify the set of all $y$-values that the function takes. From the graph, we observe that the minimum $y$-value is $2$ and the maximum $y$-value is $4$

step 4

Therefore, the range of $f(x)$ is the interval $[2, 4]$

Answer

Domain: $[-4, 6]$

Range: $[2, 4]$

Key Concept

Domain and Range of a Piecewise Function

Explanation

The domain of a function is the set of all possible input values (x-values) for which the function is defined, while the range is the set of all possible output values (y-values) that the function can take.

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