Write the equation for each transformation of f(x)= |x| described below.a. translate left 9 units, stretch vertically by a factor of 5, and translate down 23 units.

b. translate left 12 units, stretch horizontally by a factor of 4, and reflect over the x-axis.

need steps don't understand how to do!

Answers

Answer 1

Answer: okay, original equation of an absolute value function is:
a. f(x) = a |x-h| + k
a is the stretch or shrink
h is horizontal movement (watch the negative!!)
k is vertical shift

Translate left 9 units means horizontal shift so the h changes. When you move to the left, the numbers become negative so y = a|x-(-9)| + k which becomes
y = a|x+9| + k Then the vertical stretch of 5 becomes y = 5|x+9| + k And then a translation down 23 units means a negative shift down (which is your vertical shift) so:
f(x) = 5(x+9) - 23

b. translate left 12 units meaning a negative horizontal shift. y = a|x-(-12)| + k
so then it becomes y = a|x+12| + k
a stretch horizontally by 4 is your a, so y = 4|x+12| (you can just forget about the k since there is no vertical shift so your k = 0)
a reflection over the x-axis means that your horizontal axis is taken and folded and the reflection from the graph is your new graph. So basically, the whole equation becomes negative.
y = -4|x+12|

Answer 2

Answer:

Final answer:

For a, the transformed function is 5*|x+9| - 23 after translating 9 units to the left, stretching vertically by a factor of 5, and translating down 23 units. For b, the transformed function is -|(x+12)/4|, after translating 12 units to the left, stretching horizontally by a factor of 4, and reflecting over the x-axis.

Explanation:

The given function is f(x) = |x|. To write the equation for each transformation, you need to understand how they influence the function.

a. To translate the function left 9 units, the value 9 needs to be added inside the absolute value brackets creating f(x) = |x+9|. To stretch it vertically by a factor of 5, we multiply the entire function by 5 - 5 * f(x) = 5*|x+9|. Lastly, to translate down 23 units, we subtract 23 from the entire function, leading us to 5*|x+9| - 23.

b. To translate left 12 units, we change the function to |x+12|. To stretch horizontally by a factor of 4, divide the x inside the absolute value by 4, getting |(x+12)/4|. To reflect over the x-axis, we multiply the entire function by -1, leading to -|(x+12)/4|.

Learn more about Function Transformation here:

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Answers

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Answers

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Answers

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Answers

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Answers

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