Math / Algebra

QuestionIf $(-3,2)$ is a point on the graph of $y=f(x)$ , which of the following must be on the graph of $y=-f(x)$ ?
Choose the correct answer below. $(2,3)$ $(-2,-3)$ $(-3,-2)$ $(3,2)$

Studdy Solution

STEP 1

1. The function $y = -f(x)$ is a vertical reflection of the function $y = f(x)$ .
2. The point $(-3, 2)$ is on the graph of $y = f(x)$ .
3. We need to determine which point must lie on the graph of $y = -f(x)$ .

STEP 2

1. Understand the transformation from $y = f(x)$ to $y = -f(x)$ .
2. Apply the transformation to the given point.
3. Identify the correct transformed point.

STEP 3

The transformation from $y = f(x)$ to $y = -f(x)$ involves reflecting the graph over the x-axis.

STEP 4

Given the point $(-3, 2)$ on $y = f(x)$ , reflect this point over the x-axis to find the corresponding point on $y = -f(x)$ .

STEP 5

Reflecting $(-3, 2)$ over the x-axis changes the y-coordinate from $2$ to $-2$ , resulting in the point $(-3, -2)$ .

STEP 6

The point $(-3, -2)$ is the reflection of $(-3, 2)$ over the x-axis, and therefore must be on the graph of $y = -f(x)$ .
The correct answer is:
$\boxed{(-3, -2)}$

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QuestionIf $(-3,2)$ is a point on the graph of $y=f(x)$ , which of the following must be on the graph of $y=-f(x)$ ?
Choose the correct answer below. $(2,3)$ $(-2,-3)$ $(-3,-2)$ $(3,2)$

Studdy Solution

STEP 1

1. The function $y = -f(x)$ is a vertical reflection of the function $y = f(x)$ .
2. The point $(-3, 2)$ is on the graph of $y = f(x)$ .
3. We need to determine which point must lie on the graph of $y = -f(x)$ .

STEP 2

1. Understand the transformation from $y = f(x)$ to $y = -f(x)$ .
2. Apply the transformation to the given point.
3. Identify the correct transformed point.

STEP 3

The transformation from $y = f(x)$ to $y = -f(x)$ involves reflecting the graph over the x-axis.

STEP 4

Given the point $(-3, 2)$ on $y = f(x)$ , reflect this point over the x-axis to find the corresponding point on $y = -f(x)$ .

STEP 5

Reflecting $(-3, 2)$ over the x-axis changes the y-coordinate from $2$ to $-2$ , resulting in the point $(-3, -2)$ .

STEP 6

The point $(-3, -2)$ is the reflection of $(-3, 2)$ over the x-axis, and therefore must be on the graph of $y = -f(x)$ .
The correct answer is:
$\boxed{(-3, -2)}$

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QuestionIf (−3,2)(-3,2)(−3,2) is a point on the graph of y=f(x)y=f(x)y=f(x), which of the following must be on the graph of y=−f(x)y=-f(x)y=−f(x) ?Choose the correct answer below. (2,3)(2,3)(2,3) (−2,−3)(-2,-3)(−2,−3) (−3,−2)(-3,-2)(−3,−2) (3,2)(3,2)(3,2)

Studdy Solution

STEP 1

1. The function y=−f(x) y = -f(x) y=−f(x) is a vertical reflection of the function y=f(x) y = f(x) y=f(x).2. The point (−3,2)(-3, 2)(−3,2) is on the graph of y=f(x) y = f(x) y=f(x).3. We need to determine which point must lie on the graph of y=−f(x) y = -f(x) y=−f(x).

STEP 2

1. Understand the transformation from y=f(x) y = f(x) y=f(x) to y=−f(x) y = -f(x) y=−f(x).2. Apply the transformation to the given point.3. Identify the correct transformed point.

STEP 3

The transformation from y=f(x) y = f(x) y=f(x) to y=−f(x) y = -f(x) y=−f(x) involves reflecting the graph over the x-axis.

STEP 4

Given the point (−3,2)(-3, 2)(−3,2) on y=f(x) y = f(x) y=f(x), reflect this point over the x-axis to find the corresponding point on y=−f(x) y = -f(x) y=−f(x).

STEP 5

Reflecting (−3,2)(-3, 2)(−3,2) over the x-axis changes the y-coordinate from 222 to −2-2−2, resulting in the point (−3,−2)(-3, -2)(−3,−2).

STEP 6

The point (−3,−2)(-3, -2)(−3,−2) is the reflection of (−3,2)(-3, 2)(−3,2) over the x-axis, and therefore must be on the graph of y=−f(x) y = -f(x) y=−f(x). The correct answer is:(−3,−2) \boxed{(-3, -2)} (−3,−2)​

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QuestionIf $(-3,2)$ is a point on the graph of $y=f(x)$ , which of the following must be on the graph of $y=-f(x)$ ?
Choose the correct answer below. $(2,3)$ $(-2,-3)$ $(-3,-2)$ $(3,2)$

1. The function $y = -f(x)$ is a vertical reflection of the function $y = f(x)$ .
2. The point $(-3, 2)$ is on the graph of $y = f(x)$ .
3. We need to determine which point must lie on the graph of $y = -f(x)$ .

1. Understand the transformation from $y = f(x)$ to $y = -f(x)$ .
2. Apply the transformation to the given point.
3. Identify the correct transformed point.

The transformation from $y = f(x)$ to $y = -f(x)$ involves reflecting the graph over the x-axis.

Given the point $(-3, 2)$ on $y = f(x)$ , reflect this point over the x-axis to find the corresponding point on $y = -f(x)$ .

Reflecting $(-3, 2)$ over the x-axis changes the y-coordinate from $2$ to $-2$ , resulting in the point $(-3, -2)$ .

The point $(-3, -2)$ is the reflection of $(-3, 2)$ over the x-axis, and therefore must be on the graph of $y = -f(x)$ .
The correct answer is:
$\boxed{(-3, -2)}$