How many of the following statements are correct?
1. Graph of $- f (x)$ is obtained by taking the reflection of $f (x)$ about x-axis.
2. Graph of $f (- x)$ is obtained by taking the reflection of $f (x)$ about x-axis.

3. Graph of $- f (- x)$ is obtained by taking the mirror image of the graph of $f (x)$ about x-axis and then about y-axis.

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Solution

Statements one and three are correct. In statement 2, we have to take the reflection about y-axis to get $f (- x)$ .

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Similar questions

How many of the following statements are correct?
1. Graph of $- f (x)$ is obtained by taking the reflection of $f (x)$ about x-axis.
2. Graph of $f (- x)$ is obtained by taking the reflection of $f (x)$ about x-axis.

3. Graph of $- f (- x)$ is obtained by taking the mirror image of the graph of $f (x)$ about x-axis and then about y-axis.

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Graph of $| f (| x |) |$ is obtained from f(x) through the following steps.

1. Take the reflection of the part of f(x) which is below x-axis

2. Remove the part on negative x-axis

3. Take the reflection of the remaining part about y-axis

Which of the following statements is/are true about an odd function f(x)?

Q. The graph of

- f (x)

will be the mirror image of the graph of

f (x)

about the

x -

axis.

Q. While doing the transformation

f (x) \to | f (x) |

, we take the mirror image of the graph lying below x-axis and leave the other parts as it is to get the graph of f(x) from |f(x)|

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Statements one and three are correct. In statement 2, we have to take the reflection about y-axis to get f(−x).

Statements one and three are correct. In statement 2, we have to take the reflection about y-axis to get $f (- x)$ .