Question

What is the rule that defines the function represented by the table?

Answer 1

Answer:

The rule that defines the function represented by the table is:

• c. $f(x)=40(\frac{1}{4})^{x}$

Step-by-step explanation:

To identify the rule that defines the function represented by the table, you must know that $f(x) = y$, so, you can take formula by formula and replace in it the values given in the table, if the result is equal to $y$ replacing the values of $x$, you're gonna know that formula is correct. Let's do that exercise with the formulas in order:

• a. $f(x)=\frac{1}{4}(40)^{x}$

Now, we're gonna replace the variable $x$ by the first value in the table: 0

• $f(x)=\frac{1}{4}(40)^{0}$
• $f(x)=\frac{1}{4}*1$
• $f(x)=\frac{1}{4}$

How you can see in the table, exactly below the value 0 to the variable $x$ is the value to $y$ (40), how the answer with the A option doesn't result in 40, it doesn't the correct rule.

• b. $f(x)=\frac{1}{2}(40)^{x}$

We replace with the value 0 again:

• $f(x)=\frac{1}{2}(40)^{0}$
• $f(x)=\frac{1}{2}*1$
• $f(x)=\frac{1}{2}$

In this case, it neither gives us the value 40, for this reason, we pass to the next option:

• c. $f(x)=40(\frac{1}{4})^{x}$

We replace with the value 0 one more time:

• $f(x)=40(\frac{1}{4})^{0}$
• $f(x)=40*1$
• $f(x)=40$

With this option, the result is equal to the first datum, but, to check this, we can replace the same formula with one or two values more:

• $f(x)=40(\frac{1}{4})^{1}$
• $f(x)=40*(\frac{1}{4})$
• $f(x)=10$

• $f(x)=40(\frac{1}{4})^{2}$
• $f(x)=40*(\frac{1}{16})$
• $f(x)=\frac{5}{2}$

How you can see, with the C option, once you replace the value of $x$, the result is exactly the value for $y$, for this reason, the C option is the correct answer.

Answer 2

Answer:

what is the rule that defines a function represented by the table. is it increasing or decreasing