The functions y=x²

To solve this problem, we'll follow these steps:

• Step 1: Set up the equation from the function definition.
• Step 2: Solve the equation by taking the square root of both sides.
• Step 3: Identify all possible values for $x$.
• Step 4: Compare with the given answer choices.

Now, let's work through each step:

Step 1: We start with the equation given by the function $f(x) = x^2$. We know $f(?) = 16$, so we can write:

$x^2 = 16$

Step 2: To solve for $x$, we take the square root of both sides of the equation:

$x = \pm \sqrt{16}$

Step 3: Solve for $\sqrt{16}$:

The square root of 16 is 4, so:

$x = 4$ or $x = -4$

This gives us the two solutions: $x = 4$ and $x = -4$.

Step 4: Compare these solutions to the answer choices. The correct choice is:

$f(4)$ and $f(-4)$

Therefore, the solution to the problem is $f(4)$ and $f(-4)$.

To solve this problem, we'll follow these steps:

• Step 1: Substitute the given value of $x$ into the equation.
• Step 2: Perform the calculation to find $y$.

Now, let's work through each step:
Step 1: The given equation is $y = x^2$. We need to substitute $x = 2$ into this equation.

Step 2: Substitute to get $y = (2)^2$. Calculate $2 \times 2 = 4$.

Therefore, the value of $y$ when $x = 2$ is $y = 4$.

Hence, the solution to the problem is $y = 4$.

To solve this problem, we'll follow these steps:

• Step 1: Analyze the equation $y = x^2$.
• Step 2: Investigate whether a negative $y$-value is possible.

Now, let's work through each step:
Step 1: The function we have is $y = x^2$. This function is defined for all real numbers and always gives a non-negative value $y$ because squaring a real number cannot result in a negative number.

Step 2: We need to check whether $y = -2$ is possible by solving $x^2 = -2$. In the real number system, no real number $x$ satisfies this equation since the square of any real number is non-negative.
Therefore, there is no real point where $y = -2$ on the graph of the function $y = x^2$.

Therefore, the solution to the problem is No.

To solve this problem, we'll follow these steps:

• Step 1: Identify the given function and required y-value.
• Step 2: Attempt to solve $x^2 = -6$ for $x$.
• Step 3: Conclude based on the results of the equation.

Let's work through each step:

Step 1: The function we are dealing with is $y = x^2$, and we need to find $x$ such that $y = -6$.

Step 2: Substitute $-6$ for $y$, which gives us:

$x^2 = -6$

Step 3: To solve $x^2 = -6$, consider whether it is possible for a real number squared to equal a negative number. A critical point here is that the square of any real number is non-negative. Therefore, there is no real value of $x$ that satisfies $x^2 = -6$.

Thus, there is no point where $y = -6$ for the function $y = x^2$.

The correct answer is No.

To determine if the function $y = x^2$ passes through the point $(6, 36)$, follow these steps:

• Step 1: Identify the given point and function. We have $x = 6$ and we need to check if $y = 36$ when $y = x^2$.
• Step 2: Substitute $x = 6$ in the function $y = x^2$:
  $y = 6^2 = 36$.
• Step 3: Compare the calculated $y$ value (36) to the given value (36).

Since the calculated value of $y$ is equal to the given value, the function $y = x^2$ indeed passes through the point $(6, 36)$.

Therefore, the answer is Yes.