60 points and brainiest!!!!!! Pls help me

Mathematics

2 answers:

zimovet [89]3 years ago

8 0

x - 3, x < -3

x - 3, x>3

x - 3, -3 <_ x > 3

2/5, 3/6

8, 10

Svetlanka [38]3 years ago

7 0

Answers:

1.) x - 3, x < -3

2.) x - 3, x>3

3.) x - 3, -3 <_ x > 3

4.) 2/5, 3/6

5.) 8, 10

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Write an equation that represents a horizontal translation 10 units left of the graph of g(x) = |x|

Vika [28.1K]

Answer: h(x) = |x+10|

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Explanation:

To shift the graph 10 units to the left, we replace x with x+10. What's really going on is that the xy axis shifts 10 units to the right (because x is now x+10; eg, x = 2 ---> x+10 = 2+10 = 12) so it appears that the graph is moving to the left. The general rule is h(x) = g(x+10).

So,
g(x) = |x|
g(x+10) = |x+10| ... every x has been replaced with x+10
h(x) = g(x+10)
h(x) = |x+10|

We can use a graphing tool like GeoGebra to visually confirm we have the right answer (see attached). Note how a point like (0,0) on the green graph moves to (-10,0) on the red graph.