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The image of the function f(x) after vertical shrink by a factor of 1/2
and a reflection in the y-axis, followed by a translation 1 unit down
is g(x) = x² - 1
Step-by-step explanation:
Lets revise:
1. The vertical shrink
A vertical shrinking is the squeezing of the graph toward the x-axis.
if 0 < k < 1 (a fraction), the graph of y = k•f(x) is the graph of f(x) vertically
shrunk by multiplying each of its y-coordinates by k
2. The reflection
If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)
3. Vertical translation
If the function f(x) translated vertically up by m units, then its image
is g(x) = f(x) + m
If the function f(x) translated vertically down by m units, then its image
is g(x) = f(x) - m
Now let us solve the problem
∵ f(x) = x²
∵ f(x) shrunk by a factor of
∴ The image of f(x) = x²
∵ The image of f(x) reflected across y-axis
∴ The sign of x will change
∴ The new image of f(x) = (-x)²
∵ The new image of f(x) translated 1 unit down
∴ We will subtract the new image of f(x) by 1
∴ The last image of f(x) is g(x) = (-x)² - 1
<em>V.I.Note:</em>
(-x)² = x² because even exponents reject the negative sign
The image of the function f(x) after vertical shrink by a factor of 1/2
and a reflection in the y-axis, followed by a translation 1 unit down
is g(x) = x² - 1
The attached graph for more understand
Learn more:
you can learn more about transformation in brainly.com/question/2415963
#LearnwithBrainly
Answer:
The rearrangement of the terms is .
Step-by-step explanation:
The given expression is
Two terms are called like terms if they have same variables having same degree.
In the given expression 3 and -4, -6x and 3x, 4x² and -6x² are like terms.
Arrange the given terms according to their degree and arrange in this way so like terms are next to each other.
Therefore the rearrangement of the terms is .