QuestionThe tables below show the values of four different functions for given values of .
\begin{tabular}{|c|c|}
\hline & \\
\hline 1 & 12 \\
\hline 2 & 19 \\
\hline 3 & 26 \\
\hline 4 & 33 \\
\hline
\end{tabular}
\begin{tabular}{|c|c|}
\hline & \\
\hline 1 & -1 \\
\hline 2 & 1 \\
\hline 3 & 5 \\
\hline 4 & 13 \\
\hline
\end{tabular}
\begin{tabular}{|c|c|}
\hline & \\
\hline 1 & 9 \\
\hline 2 & 12 \\
\hline 3 & 17 \\
\hline 4 & 24 \\
\hline
\end{tabular}
\begin{tabular}{|c|c|}
\hline & \\
\hline 1 & -2 \\
\hline 2 & 4 \\
\hline 3 & 14 \\
\hline 4 & 28 \\
\hline
\end{tabular}
Which table represents a linear finction?
(1)
(3)
(2)
(4)
Studdy Solution
STEP 1
What is this asking? Which of these tables shows a straight line when you graph it? Watch out! Don't just look at the numbers themselves, look at how they change!
STEP 2
1. Check Table f(x)
2. Check Table g(x)
3. Check Table h(x)
4. Check Table k(x)
STEP 3
Let's peep at the changes between the \(f(x)\) values in the first table.
From \(x=1\) to \(x=2\), \(f(x)\) goes from **12** to **19**, a jump of \(19 - 12 = 7\).
From \(x=2\) to \(x=3\), \(f(x)\) increases by \(26 - 19 = 7\).
And, from \(x=3\) to \(x=4\), it increases by \(33 - 26 = 7\) again!
The **constant difference** of **7** tells us this is a **linear function**!
Woohoo!
STEP 4
Now, let's scope out the second table, \(g(x)\).
From \(x=1\) to \(x=2\), \(g(x)\) changes by \(1 - (-1) = 2\).
From \(x=2\) to \(x=3\), it changes by \(5 - 1 = 4\).
Hmm, \(2\) and \(4\) are not the same, so this isn't a linear function.
STEP 5
On to table number three, \(h(x)\)!
From \(x=1\) to \(x=2\), \(h(x)\) changes by \(12 - 9 = 3\).
From \(x=2\) to \(x=3\), it changes by \(17 - 12 = 5\).
Nope, not linear!
STEP 6
Finally, let's investigate \(k(x)\).
From \(x=1\) to \(x=2\), \(k(x)\) changes by \(4 - (-2) = 6\).
From \(x=2\) to \(x=3\), it changes by \(14 - 4 = 10\).
No constant change here, so not a linear function.
STEP 7
The table that represents a linear function is \(f(x)\), so the answer is (1).
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