Question

Which of the following ordered pairs belongs to the graph of f(x)

Answer 1

Answer:

The second choice, $(-1,\, 12)$.

Step-by-step explanation:

Note, that the expression $y = f(x)$ is an equation. A point $(x,\, y)$ is on the graph of $y = f(x)\!$ if and only if the value of $x$ and $y$ satisfy this equation; that is: in other words, the $y\!$-coordinate of that point (the second number in the tuple) should be equal to $f(x)$, which is equal to $(-3\, x +9)$ (evaluated where $x\!$ is equal to the first number in the tuple.

For each tuple in the choices, calculate the value of $f(x)$ where $x$ is equal to the first number of each tuple. Compare the result to the second number in that tuple. That choice corresponds to a valid point on $y = f(x)$ only if these two numbers match.

• First choice: $x = 1$, $f(x) = f(1) = -3 + 9 = 6$. That's not the same as the second number, $-10$. Therefore, this point isn't on the graph of $y = f(x)$.
• Second choice: $x = -1$, $f(x) = f(-1) = (-3)\times (-1) + 9 = 3 + 9 = 12$. That matches the second number in the tuple. Therefore, this point is on the graph of $y = f(x)$.
• Third choice: $x = 2$, $f(x) = f(2) = (-3)\times 2 + 9 = 3$. That's not the same as the second number, $(-3)$. Therefore, this point isn't on the graph of $y = f(x)$.
• Fourth choice: $x = -2$, $f(x) = f(-2) = (-3)\times (-2) + 9 = 15$. That's not the same as the second number, $13$. Therefore, this point isn't on the graph of $y = f(x)$.