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sasho [114]
3 years ago
13

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

Mathematics
2 answers:
cupoosta [38]3 years ago
5 0

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, <u>the C option is the correct answer</u>.

jeyben [28]3 years ago
4 0

Answer:

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

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