SOLUTION: I've tried everything and I can't get this problem. Its an algebra 2 question and it says "If h(x) is a horizontal translation 8 units left of f(x)=-2x-5, what is the rule for h(x)

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Question 957587: I've tried everything and I can't get this problem. Its an algebra 2 question and it says "If h(x) is a horizontal translation 8 units left of f(x)=-2x-5, what is the rule for h(x)? Its an multiple choice A)h(x)=-2x+1 B)h(x)=-2x-13 C)h(x)=-2x+3 D)h(x)=2x+8
Found 2 solutions by stanbon, Theo:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
"If h(x) is a horizontal translation 8 units left of f(x)=-2x-5, what is the rule for h(x)? Its an multiple choice
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You add to "the variable expression" to move the graph left.
Assuming that f(x) = -2x - 5 , then h(x) = -2(x+8)-5 = -2x-21
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Comment::
If your f(x) = -2(x-5) your answer would be h(x) = -2(x-5+8) = -2(x+3)
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Cheers,
Stan H.
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A)h(x)=-2x+1
B)h(x)=-2x-13
C)h(x)=-2x+3
D)h(x)=2x+8

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
here's a reference.

https://sites.google.com/site/mymathclassroom/algebra/horizontal-translations-of-graphs---why-we-have-to-subtract-instead-of-add-in-order-for-the-graph-to-shift-to-the-right

if you have a horizontal shift to the left, the you would need to replace x with x + 8.

f(x) = -2x - 5 would lead to:

h(x) = -2(x+8) - 5 which, when simplified, would lead to:

h(x) = -2x - 16 - 5 which would then lead to:

h(x) = -2x - 21.

unfortunately, that is not one of your selections.

I graphed the f(x) = y = -2x-5 and h(x) = y = -2x-21 which are shown below.

the black line is f(x) and the blue line is h(x).

you can see from the graph that the blue line is horizontally shifted to the left of the black line by 8 units.

that meets the requirements of the problem but is not one of the selections shown as your options.