Question

Math

Posted 2 months ago

```
Refer to the graph of the function $f$ in the following figure.
(a) Find the value of $f(9)$.
$f(9)=$
$\square$
(b) Find the values of $x$ corresponding to the point(s) on the graph of $f$ located at a height of 5 units above the $x$-axis.
$\begin{array}{l}
x=\square \text { (smaller value) } \\
x=\square \text { (larger value) }
\end{array}$
(smaller value) (larger value)
(c) Find the point on the $x$-axis at which the graph of $f$ crosses it.
$x=$
$\square$
What is the value of $f(x)$ at this point?
(c) Find the point on the $x$-axis at which the graph of $f$ crosses it.
$x=$
$\square$
What is the value of $f(x)$ at this point?
$f(x)=$
$\square$
(d) Find the domain and range of $f$. (Enter your answers using interval notation.) domain $\square$
range $\square$
```

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Answer from Sia

Posted 2 months ago

Solution by Steps

step 1

To find the value of $f(9)$, we look at the graph where $x = 9$. From the graph, we see that the point corresponding to $x = 9$ is $(9, 1)$. Therefore, $f(9) = 1$

step 2

To find the values of $x$ corresponding to the point(s) on the graph of $f$ located at a height of 5 units above the $x$-axis, we look for points where $y = 5$. From the graph, we see that the points are $(4, 5)$. Therefore, the smaller value of $x$ is $4$ and there is no larger value

step 3

To find the point on the $x$-axis at which the graph of $f$ crosses it, we look for points where $y = 0$. From the graph, we see that the points are $(2, 0)$. Therefore, $x = 2$

step 4

The value of $f(x)$ at the point where the graph crosses the $x$-axis is $0$

step 5

To find the domain and range of $f$, we observe the graph. The domain is the set of all $x$ values for which the function is defined, which is $[-2, 9]$. The range is the set of all $y$ values that the function takes, which is $[-3, 6]$

[question number] Answer

A

Key Concept

Graph Analysis

Explanation

To find specific values and points on a graph, observe the coordinates and the behavior of the function as it intersects the axes and reaches certain heights.

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