Transformations: 동영상 및 연습문제

If the function $g\(\left\)(x\(\right\))=x^2+4$ is graphed, compared to $y=x^2$, in which direction and by how many units is the graph shifted?

If the function $h\(\left\)(x\(\right\))=\(\left\)(x-2\(\right\))^2$ is graphed, compared to $y=x^2$, in which direction and by how many units is the graph shifted?

If the function $h\(\left\)(x\(\right\))=-2x^2$ is graphed, how does its graph compare to the graph of $y=2x^2$?

If the function $g\(\left\)(x\(\right\))=6\(\sqrt{-x}\)$ is graphed, how does its graph compare to the graph of $y=6\(\sqrt{x}\)$?

Which of the following statements best describes the relationship between the graphs of $y=12x^3$ and $y=x^3$?

Plot the given function. 

g(x) = 15|x|

Plot the given function. 

g(x) = (7/8)|x|

Plot the given function. 

g(x) = 12x²

Plot the given function. 

g(x) = (1/12)x²

Plot the given function. 

g(x) = -(1/12)x²

Plot the given function. 

g(x) = -15|x|

Plot the given function. 

f(x) = |(-7/8)x|

Plot the given function. 

g(x) = √(11x)

Plot the given function. 

g(x) = -√-11x

Which of the following transformations is a type of reflection?

If the function f(x) = x^2 is shifted 3 units to the right and 2 units up, which of the following is the equation of the transformed function?

What is the function notation for reflecting the function f(x) = x^3 over the y-axis?

Given the function g(x) = |x|, what is the resulting function if it is shifted left by 4 units and down by 5 units?

What happens to the function f(x) = sin(x) if it undergoes a vertical stretch by a factor of 3?

Which of the following sequences of transformations is equivalent to first reflecting over the x-axis and then shifting up by 2 units?

The function f(x) = √(x + 4) is transformed to g(x) = √(x + 4) - 3. What is the domain and range of g(x)?

If the function f(x) = x^2 is stretched vertically by a factor of 2 and then shifted down by 3 units, what is the equation of the new function?

Which of the following is a vertical shift transformation?

If the graph of f(x) = x^3 is shifted 2 units down, what is the equation of the new function?

Which of the following represents a horizontal shift of 3 units to the left for the function f(x) = x^2?

For the function g(x) = cos(x), what is the equation after it is shifted π/4 units to the right and 1 unit up?

If the function f(x) = e^x is reflected over the x-axis, what is the resulting function?

How does the graph of f(x) = 1/x change with a horizontal compression by a factor of 2?

What is the result of first reflecting f(x) = √x over the y-axis and then shifting it 3 units up?

The point $(-3,4)$ lies on the graph of $y=f\left(x\right)$. After reflecting the graph over the x-axis and then shifting it right 5 units and down 2 units, find the y-coordinate of the image of this point.