What equation represents the following transformation of y = (x + 5) ^ 2 :
a horizontal compression by a factor of 3
a. y=-3(x+5)²
b. y=3(x+5)²
c. y = (3x + 15) ^ 2
d. y = (3x + 5) ^ 2
11 answers
d. y = (3x + 5) ^ 2
What equation represents the following transformation of y = (x + 5) ^ 2 :
a horizontal compression by a factor of 3
a. y=-3(x+5)²
b. y=3(x+5)²
c. y = (3x + 15) ^ 2
d. y = (3x + 5) ^ 2
With explanation plz
a horizontal compression by a factor of 3
a. y=-3(x+5)²
b. y=3(x+5)²
c. y = (3x + 15) ^ 2
d. y = (3x + 5) ^ 2
With explanation plz
The equation that represents a horizontal compression by a factor of 3 is given by:
y = (1/3)(x + 5)^2
To see why, we can use the general formula for a horizontal compression/stretch:
y = f((1/k)(x - h)) + k
where f(x) is the original function, k is the vertical compression/stretch factor (which we will keep as 1 for now), h is the horizontal shift, and 1/k is the horizontal compression/stretch factor.
In this case, f(x) = (x + 5)^2, h = -5 (since the function is shifted left by 5 units), and 1/k = 1/3 (since the function is horizontally compressed by a factor of 3). Plugging these values into the formula, we get:
y = (x + 5)^2 → f(x) = (x + 5)^2
1/k = 1/3
h = -5
k = 1 (no vertical compression/stretch)
y = f((1/k)(x - h)) + k
= (x + 5)^2 → replace f(x) with (x + 5)^2
(1/3)(x - (-5)) + 1 → simplify the expression inside f()
= (1/3)(x + 5)^2 + 1 → distribute the 1/3
Therefore, the equation that represents a horizontal compression by a factor of 3 is:
y = (1/3)(x + 5)^2
y = (1/3)(x + 5)^2
To see why, we can use the general formula for a horizontal compression/stretch:
y = f((1/k)(x - h)) + k
where f(x) is the original function, k is the vertical compression/stretch factor (which we will keep as 1 for now), h is the horizontal shift, and 1/k is the horizontal compression/stretch factor.
In this case, f(x) = (x + 5)^2, h = -5 (since the function is shifted left by 5 units), and 1/k = 1/3 (since the function is horizontally compressed by a factor of 3). Plugging these values into the formula, we get:
y = (x + 5)^2 → f(x) = (x + 5)^2
1/k = 1/3
h = -5
k = 1 (no vertical compression/stretch)
y = f((1/k)(x - h)) + k
= (x + 5)^2 → replace f(x) with (x + 5)^2
(1/3)(x - (-5)) + 1 → simplify the expression inside f()
= (1/3)(x + 5)^2 + 1 → distribute the 1/3
Therefore, the equation that represents a horizontal compression by a factor of 3 is:
y = (1/3)(x + 5)^2
AAAaannndd the bot gets it wrong yet again!
NO. Horizontal compress by a factor of 3 is given by replacing x by 3x.
So, to compress y = (x+5)^2 by 3, you need
y = (3(x+5))^2
y = (1/3)(x + 5)^2 is a vertical compression
y = (3x + 5)^2 = (3(x + 5/3))^2 changes the horizontal shift from 5 to 5/3
And why would you answer the same question in two different ways? Sounds like you not only don't know how to do the math, but you aren't even sure of your own so-called skills.
NO. Horizontal compress by a factor of 3 is given by replacing x by 3x.
So, to compress y = (x+5)^2 by 3, you need
y = (3(x+5))^2
y = (1/3)(x + 5)^2 is a vertical compression
y = (3x + 5)^2 = (3(x + 5/3))^2 changes the horizontal shift from 5 to 5/3
And why would you answer the same question in two different ways? Sounds like you not only don't know how to do the math, but you aren't even sure of your own so-called skills.
I apologize for the mistake in my previous answer. You are correct that a horizontal compression by a factor of 3 is achieved by replacing x with 1/3x.
Therefore, the equation that represents a horizontal compression of y = (x + 5)^2 by a factor of 3 is:
y = ((1/3)x + 5)^2
Again, I apologize for any confusion or frustration my previous answer may have caused. As an AI language model, I strive to provide accurate answers to the best of my ability.
Therefore, the equation that represents a horizontal compression of y = (x + 5)^2 by a factor of 3 is:
y = ((1/3)x + 5)^2
Again, I apologize for any confusion or frustration my previous answer may have caused. As an AI language model, I strive to provide accurate answers to the best of my ability.
still wrong, but I give up...
I apologize once again for my mistake. The correct equation that represents a horizontal compression by a factor of 3 for y = (x + 5)^2 is y = (1/9)(3x + 15)^2.
To explain further, a horizontal compression by a factor of 3 means that the original x-values are multiplied by 1/3 to get the new x-values. So, we can rewrite the original equation y = (x + 5)^2 as y = ((1/3)x + 5)^2 after applying this transformation.
Then, we can simplify this equation by factoring out the 1/9 from the squared term to obtain y = (1/9)(3x + 15)^2, which represents the horizontal compression by a factor of 3.
Again, I apologize for any confusion and I hope this answer clears up any doubts you may have had.
To explain further, a horizontal compression by a factor of 3 means that the original x-values are multiplied by 1/3 to get the new x-values. So, we can rewrite the original equation y = (x + 5)^2 as y = ((1/3)x + 5)^2 after applying this transformation.
Then, we can simplify this equation by factoring out the 1/9 from the squared term to obtain y = (1/9)(3x + 15)^2, which represents the horizontal compression by a factor of 3.
Again, I apologize for any confusion and I hope this answer clears up any doubts you may have had.
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1 answer