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Just an easy question for 100 Points!
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Just an easy question for 100 Points! Check my other easy 100 point questions :)-example-1
User John Ferguson
by
2.7k points

2 Answers

20 votes
20 votes

#1

y=x+5

  • Shifted 5units left

#2

y=3/8

  • Horizontally Streched by a factor 8/3 parallel to x axis

#3

  • y=-x-2

Reflection by y axis as x will be negative and shifting 2 units right

#4

y=6x+1

  • vertically streched by a factor 6 and shifting 1 units left

#5

y=x-11

  • Shifting 11 units left

#6

y=8x

Horizontally streched by 1/8 factor

User Minkyu Kim
by
2.8k points
12 votes
12 votes

Answer:

1. Translated 5 units left.

2. Vertical stretch by a factor of 3/8.

3. Reflection in the x-axis, then translated 2 units down.

4. Vertical stretch by a factor of 6, then translated 1 unit up.

5. Translated 11 units down.

6. Vertical stretch by a factor of 8.

7. Vertical stretch by a factor of 1/3, then reflection in the x-axis.

Explanation:

Transformations

For a > 0


f(x+a) \implies f(x) \: \textsf{translated $a$ units left}.


f(x-a) \implies f(x) \: \textsf{translated $a$ units right}.


f(x)+a \implies f(x) \: \textsf{translated $a$ units up}.


f(x)-a \implies f(x) \: \textsf{translated $a$ units down}.


a\:f(x) \implies f(x) \: \textsf{stretched parallel to the $y$-axis (vertically) by a factor of $a$}.


f(ax) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $(1)/(a)$}.


-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}.


f(-x) \implies f(x) \: \textsf{reflected in the $y$-axis}.

Parent function:


y=x


\textsf{1.} \quad y=x+5

Translated 5 units left.


\textsf{2.} \quad y=(3)/(8)x

Vertical stretch by a factor of 3/8.


\textsf{3.} \quad y=-x-2

Reflection in the x-axis, then translated 2 units down.


\textsf{4.} \quad y=6x+1

Vertical stretch by a factor of 6, then translated 1 unit up.


\textsf{5.} \quad y=x-11

Translated 11 units down.


\textsf{6.} \quad y=8x

Vertical stretch by a factor of 8.


\textsf{7.} \quad y=-(1)/(3)x

Vertical stretch by a factor of 1/3, then a reflection in the x-axis.

User Rehan Shikkalgar
by
2.9k points