Question

Question
What is the starting value in the table that is needed to graph the equation h(x)= √-2x + 4
?(1 point)
Responses

2
2

-2
-2

−1/2
negative 1 half

1/2

Answer 1

To find the starting value (or \( x \)-value) in the equation \( h(x) = \sqrt{-2x + 4} \), we need to determine the value where the expression inside the square root becomes non-negative, as the square root of a negative number is not defined in the realm of real numbers.

Set the expression inside the square root greater than or equal to zero:

\[
-2x + 4 \geq 0
\]

Now, solve for \( x \):

1. Subtract 4 from both sides:
\[
-2x \geq -4
\]

2. Divide both sides by -2 (remember that this reverses the inequality):
\[
x \leq 2
\]

This means that the starting value we can graph (the maximum \( x \)-value allowed) is \( x = 2 \).

When \( x = 2 \):
\[
h(2) = \sqrt{-2(2) + 4} = \sqrt{0} = 0
\]

At \( x = 2 \), the function \( h(x) \) is defined and gives the output of \( h(2) = 0 \).

So based on this analysis, the correct choice is:

**2**