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 $y = 4$.

The problem asks us to find an $x$ such that in the function $y = x^2$, the value of $y$ becomes 16. To do this, we'll substitute $y = 16$ into the equation and solve for $x$.

1. Start with the equation of the function:

$y = x^2$

2. Substitute $y = 16$ into the equation:

$16 = x^2$

3. Solve $x^2 = 16$ for $x$:

• Take the square root of both sides to solve for $x$:
• $x = \pm \sqrt{16}$
• This gives $x = 4$ or $x = -4$

4. Identify the points on the function for these values of $x$:

• For $x = 4$, the point is $(4, 16)$.
• For $x = -4$, the point is $(-4, 16)$, but this is not provided in the choice list.

Among the given options, the point we find in the choices is:

$(4, 16)$

Therefore, the correct answer is the choice that corresponds with this point:

$(4,16)$

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.

To determine if there is a point on the graph of the parabola $y = x^2$ where $y = 4$, we need to find values of $x$ that satisfy the equation $x^2 = 4$.

Let's solve the equation step by step:

• Set the equation: $x^2 = 4$.
• Take the square root of both sides to solve for $x$:
• $x = \sqrt{4}$ or $x = -\sqrt{4}$.
• This gives us $x = 2$ or $x = -2$.

Therefore, the points on the graph where $y = 4$ are $(2, 4)$ and $(-2, 4)$.

This matches the provided correct answer of $(2, 4)$ and $(-2, 4)$.

Therefore, the correct solution is the point set $(2, 4)$ and $(-2, 4)$.