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Here is a table of values for [tex]\( y=f(x) \)[/tex]:

[tex]\[
\begin{array}{|c|c|c|c|c|c|c|c|c|c|}
\hline
x & 0 & 5 & 10 & 15 & 20 & 25 & 30 & 35 & 40 \\
\hline
f(x) & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 \\
\hline
\end{array}
\][/tex]

Mark the statements that are true:

A. The domain for [tex]\( f(x) \)[/tex] is the set [tex]\(\{0, 5, 10, 15, 20, 25, 30, 35, 40\}\)[/tex].

B. The range for [tex]\( f(x) \)[/tex] is [tex]\(\{5, 6, 7, 8, 9, 10, 11, 12, 13\}\)[/tex].

C. [tex]\( f(5)=6 \)[/tex].

D. [tex]\( f(15)=8 \)[/tex].

Sagot :

GinnyAnswer
Let's analyze each statement based on the given table of values for [tex]\( f(x) \)[/tex].

### Statement A: The domain for [tex]\( f(x) \)[/tex] is the set [tex]\(\{5, 6, 7, 8, 9, 10, 11, 12, 13\}\)[/tex].

The domain of a function consists of all the input values (or [tex]\( x \)[/tex]-values) for which the function is defined. From the table, the [tex]\( x \)[/tex]-values are [tex]\(\{0, 5, 10, 15, 20, 25, 30, 35, 40\}\)[/tex]. These input values are different from the set given in statement A.

So, Statement A is false.

### Statement B: The range for [tex]\( f(x) \)[/tex] is all real numbers.

The range of a function consists of all the output values (or [tex]\( f(x) \)[/tex]-values) that the function can take. From the table, the [tex]\( f(x) \)[/tex]-values are [tex]\(\{5, 6, 7, 8, 9, 10, 11, 12, 13\}\)[/tex]. These are specific integers and do not cover all real numbers.

So, Statement B is false.

### Statement C: [tex]\( f(5) = 6 \)[/tex]

To verify this statement, we look at the value of [tex]\( f(x) \)[/tex] when [tex]\( x = 5 \)[/tex] from the table. The corresponding [tex]\( f(x) \)[/tex] value is 6.

So, Statement C is true.

### Statement D: [tex]\( f(15) = 8 \)[/tex]

To verify this statement, we look at the value of [tex]\( f(x) \)[/tex] when [tex]\( x = 15 \)[/tex] from the table. The corresponding [tex]\( f(x) \)[/tex] value is 8.

So, Statement D is true.

The correct marking for the statements are:

- A: False
- B: False
- C: True
- D: True
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