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NO LINKS! Please help me with these problems​

NO LINKS! Please help me with these problems​-example-1
User Amelia
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2 Answers

1 vote

Answer:

4. Translated 6 units left and 1 unit down.

5. Translated 3 units right and stretched vertically by a factor of 2.

Step-by-step explanation:

Transformations


\textsf{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}

Question 4

Parent function:


f(x)=x^2

Translated 6 units left:

Add 6 to the x-variable of the function:


\implies f(x+6)=(x+6)^2

Translated 1 unit down:

Subtract 1 from the function:


\implies f(x+6)-1=(x+6)^2-1

Question 5

Parent function:


f(x)=|x|

Translated 3 units right:

Subtract 3 from the x-variable of the function:


\implies f(x-3)=|x-3|

Stretched vertically by a factor of 2:

Multiply the function by 2:


\implies 2f(x-3)=2|x-3|

User Michael Grogan
by
8.4k points
5 votes

Answers in bold:

Problem 4) Shift 6 units left, 1 unit down

Problem 5) Shift 3 units right. Vertically stretch by a factor of 2.

The graphs are below.

==========================================================

Step-by-step explanation:

In problem 4, the parent function is y = x^2

Replace every x with (x+6) and it will shift the parabola 6 units left. Why left instead of right? It's because the xy axis is moving 6 units to the right. Each old input x is now 6 units larger to get x+6. The xy axis moving 6 units right gives the illusion the curve shifts 6 units left. It's a bit backwards I know.

Luckily the -1 at the end is straight forward and it shifts everything down by 1 unit. This is because we subtract 1 from the y coordinate.

So that's how we get the "6 units left, 1 unit down" translation. No horizontal nor vertical dilations occur.

I recommend using GeoGebra or Desmos or similar to graph out the two equations, to see the comparison.

---------------------------------

For problem 5, the parent function is y = |x|

Replacing every x with x-3 means that the xy grid moves 3 units left. That gives the illusion the V shaped curve is moving 3 units right.

The 2 out front will double each y coordinate. This visually stretches the graph by a factor of 2. It is now twice as tall as it was before. This is equivalent to doing a horizontal compression (since the graph is more skinny now).

NO LINKS! Please help me with these problems​-example-1
NO LINKS! Please help me with these problems​-example-2
User Barelyknown
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8.6k points

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