Math / Algebra

QuestionDecide whether the following statement is true or false. The graph of $y=-f(x)$ is the reflection about the $x$ -axis of the graph of $y=f(x)$ .
Choose the correct answer below. False True

Studdy Solution

STEP 1

1. The function $y = f(x)$ is a generic function.
2. The transformation $y = -f(x)$ involves multiplying the output of the function by $-1$ .
3. Reflection about the $x$ -axis involves flipping the graph vertically.

STEP 2

1. Understand the transformation $y = -f(x)$ .
2. Analyze the effect of the transformation on the graph.
3. Compare the transformation to the definition of reflection about the $x$ -axis.
4. Decide if the statement is true or false.

STEP 3

Understand the transformation $y = -f(x)$ :
When we transform $y = f(x)$ to $y = -f(x)$ , we are multiplying the output of the function by $-1$ . This means that for every point $(x, y)$ on the graph of $y = f(x)$ , the corresponding point on the graph of $y = -f(x)$ will be $(x, -y)$ .

STEP 4

Analyze the effect of the transformation on the graph:
The transformation $y = -f(x)$ changes each $y$ -coordinate to its negative, effectively flipping the graph over the $x$ -axis. This means that if a point is above the $x$ -axis in the original graph, it will be below the $x$ -axis in the transformed graph, and vice versa.

STEP 5

Compare the transformation to the definition of reflection about the $x$ -axis:
Reflection about the $x$ -axis involves flipping the graph vertically, which means every point $(x, y)$ on the graph of $y = f(x)$ is transformed to $(x, -y)$ . This is exactly what happens when we apply the transformation $y = -f(x)$ .

STEP 6

Decide if the statement is true or false:
Since the transformation $y = -f(x)$ results in a graph that is the reflection of $y = f(x)$ about the $x$ -axis, the statement is true.
The statement is $\boxed{\text{True}}$ .

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QuestionDecide whether the following statement is true or false. The graph of $y=-f(x)$ is the reflection about the $x$ -axis of the graph of $y=f(x)$ .
Choose the correct answer below. False True

Studdy Solution

STEP 1

1. The function $y = f(x)$ is a generic function.
2. The transformation $y = -f(x)$ involves multiplying the output of the function by $-1$ .
3. Reflection about the $x$ -axis involves flipping the graph vertically.

STEP 2

1. Understand the transformation $y = -f(x)$ .
2. Analyze the effect of the transformation on the graph.
3. Compare the transformation to the definition of reflection about the $x$ -axis.
4. Decide if the statement is true or false.

STEP 3

Understand the transformation $y = -f(x)$ :
When we transform $y = f(x)$ to $y = -f(x)$ , we are multiplying the output of the function by $-1$ . This means that for every point $(x, y)$ on the graph of $y = f(x)$ , the corresponding point on the graph of $y = -f(x)$ will be $(x, -y)$ .

STEP 4

STEP 5

STEP 6

Decide if the statement is true or false:
Since the transformation $y = -f(x)$ results in a graph that is the reflection of $y = f(x)$ about the $x$ -axis, the statement is true.
The statement is $\boxed{\text{True}}$ .

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QuestionDecide whether the following statement is true or false. The graph of y=−f(x)y=-f(x)y=−f(x) is the reflection about the xxx-axis of the graph of y=f(x)y=f(x)y=f(x).Choose the correct answer below. False True

Studdy Solution

STEP 1

1. The function y=f(x) y = f(x) y=f(x) is a generic function.2. The transformation y=−f(x) y = -f(x) y=−f(x) involves multiplying the output of the function by −1-1−1.3. Reflection about the x x x-axis involves flipping the graph vertically.

STEP 2

1. Understand the transformation y=−f(x) y = -f(x) y=−f(x).2. Analyze the effect of the transformation on the graph.3. Compare the transformation to the definition of reflection about the x x x-axis.4. Decide if the statement is true or false.

STEP 3

STEP 4

STEP 5

STEP 6

Decide if the statement is true or false:Since the transformation y=−f(x) y = -f(x) y=−f(x) results in a graph that is the reflection of y=f(x) y = f(x) y=f(x) about the x x x-axis, the statement is true. The statement is True\boxed{\text{True}}True​.

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QuestionDecide whether the following statement is true or false. The graph of $y=-f(x)$ is the reflection about the $x$ -axis of the graph of $y=f(x)$ .
Choose the correct answer below. False True

1. The function $y = f(x)$ is a generic function.
2. The transformation $y = -f(x)$ involves multiplying the output of the function by $-1$ .
3. Reflection about the $x$ -axis involves flipping the graph vertically.

1. Understand the transformation $y = -f(x)$ .
2. Analyze the effect of the transformation on the graph.
3. Compare the transformation to the definition of reflection about the $x$ -axis.
4. Decide if the statement is true or false.

Decide if the statement is true or false:
Since the transformation $y = -f(x)$ results in a graph that is the reflection of $y = f(x)$ about the $x$ -axis, the statement is true.
The statement is $\boxed{\text{True}}$ .