Question

Which represents the reflection of f(x) = StartRoot x EndRoot over the x-axis? A 2-column table has 4 rows. The first column is labeled x with entries negative 1, 0, 1, 4. The second column is labeled f (x) with entries undefined, 0, negative 1, negative 2. A 2-column table has 4 rows. The first column is labeled x with entries negative 1, 0, 1, 4. The second column is labeled f (x) with entries 1, 0, undefined, undefined. On a coordinate plane, an absolute value graph starts at (0, 0) and goes down and to the left through (negative 4, negative 2). On a coordinate plane, an absolute value graph starts at (0, 0) and goes down and to the right through (2, negative 4).

Answer 1

The function that represents the reflection of f(x) over the x-axis is $g(x) = -\sqrt x$

The function is given as:

$f(x)=\sqrt{x}$

The rule of reflection over the x-axis is:

$(x,y) \to (x,-y)$

So, we have:

$g(x) = -f(x)$

Substitute $f(x)=\sqrt{x}$ in the above equation

So, we have:

$g(x) = -\sqrt x$

Hence, the function that represents the reflection of f(x) over the x-axis is $g(x) = -\sqrt x$

This is represented by option (a)

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Answer 2

The function that represents the reflection of f(x) over the x-axis is $g(x)=-\sqrt{x}$.

The function is  $f(x)=\sqrt{x}$.

Now, the rule of reflection over the x-axis is (x,y) becomes (x,-y).

So, $g(x)=-f(x)$

Now putting the value of $f(x)=\sqrt{x}$ in above expression, we get

$g(x)=-\sqrt{x}$

Hence, the function that represents the reflection of f(x) over the x-axis is $g(x)=-\sqrt{x}$.

The correct option is A.

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