Question

The coordinate P(−2,7) is reflected over the y-axis. State the coordinate of P′ .(1 point)
Responses

P′(2,7)
upper P prime left parenthesis 2 comma 7 right parenthesis

P′(2,−7)
upper P prime left parenthesis 2 comma negative 7 right parenthesis

P′(7,2)
upper P prime left parenthesis 7 comma 2 right parenthesis

P′(−2,−7)

Answer 1

When a point is reflected over the y-axis, the x-coordinate changes sign while the y-coordinate remains the same.

For the point \( P(-2, 7) \):

- The x-coordinate \(-2\) becomes \(2\) (changing the sign).
- The y-coordinate \(7\) remains \(7\).

Thus, the reflected point \( P' \) is \( P'(2, 7) \).

So, the correct response is:

**P′(2, 7)**.

Answer 2

The function f(x)=(x+1)2 is reflected over the x-axis to create g(x) . Identify the equation for g(x) .(1 point)
Responses

g(x)=(−x−1)2
g left parenthesis x right parenthesis equals left parenthesis negative x minus 1 right parenthesis squared

g(x)=−x2+1
g left parenthesis x right parenthesis equals negative x squared plus 1

g(x)=(−x+1)2
g left parenthesis x right parenthesis equals left parenthesis negative x plus 1 right parenthesis squared

g(x)=−(x+1)2

Answer 3

To reflect a function \( f(x) \) over the x-axis, you negate the entire function.

The given function is:

\[
f(x) = (x + 1)^2
\]

When we reflect this function over the x-axis, we replace \( f(x) \) with \(-f(x)\):

\[
g(x) = -f(x) = -((x + 1)^2)
\]

Therefore, the equation for \( g(x) \) is:

\[
g(x) = -(x + 1)^2
\]

So, the correct response is:

**g(x) = −(x + 1)²**.

Answer 4

The function f(x)=−2x+1 is linear. Select the function g(x) based on the rule rx−axis .(1 point)
Responses

g(x)=−2x−1
g left parenthesis x right parenthesis equals negative 2 x minus 1

g(x)=2x+1
g left parenthesis x right parenthesis equals 2 x plus 1

g(x)=2x−1
g left parenthesis x right parenthesis equals 2 x minus 1

g(x)=−(2x−1)

Answer 5

To reflect the function \( f(x) = -2x + 1 \) over the x-axis, you negate the entire function.

Thus, the reflection rule gives us:

\[
g(x) = -f(x) = -(-2x + 1)
\]

This simplifies to:

\[
g(x) = 2x - 1
\]

So the correct response is:

**g(x) = 2x - 1**.