Question

1.)

Answer 1

a. f(x) is the image of the parent function after stretched vertically by

factor 3, then translated 2 units right and 6 units up

b. g(x) is the image of the parent function after stretched vertically by

factor 2, followed by reflection across the x-axis, then translated

1 unit left and 3 units up

c. n(x) is the image of the parent function after reflection across the

x-axis, then translated 7 units right and 2 units down

Step-by-step explanation:

Let us revise some transformation of the function  f(x)

• If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)  
• If the function f(x) translated horizontally to the left by h units, then  its image is g(x) = f(x + h)
• If the function f(x) translated vertically up by k units, then its image is  g(x) = f(x) + k  
• If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) – k  
• A vertical stretching is the stretching of the graph away from the  x-axis,  If m > 1, the graph of y = m • f(x) is the graph of f(x) vertically stretched by multiplying each of its y-coordinates by m.  
• A vertical compression is the squeezing of the graph toward  the x-axis,  if 0 < m < 1 (a fraction), the graph of y = m • f(x) is the graph of f(x) vertically compressed by multiplying each of its y-coordinates by m.  
• If m should be negative, the vertical stretch or compress is followed  by a reflection across the x-axis.  

The parent quadratic function is q(x) = x²

a.

∵ q(x) = x²

∵ f(x) = 3(x - 2)² + 6

∴ m = 3 , h = 2 , k = 6

∵ m > 1

∴ q(x) is stretched vertically by scale factor 3

∵ h = 2

∴ q(x) is translated 2 units to the right

∵ k = 6

∴ q(x) is translated 6 units up

f(x) is the image of the parent function after stretched vertically by

factor 3, then translated 2 units right and 6 units up

b.

∵ q(x) = x²

∵ g(x) = -2(x + 1)² + 3

∴ m = -2 , h = -1 , k = 3

∵ m is negative

∵ ImI > 1

∴ q(x) is stretched vertically by factor 2 and followed by reflection

   across the x-axis

∵ h = -1

∴ q(x) is translated 1 units to the left

∵ k = 3

∴ q(x) is translated 3 units up

g(x) is the image of the parent function after stretched vertically by

factor 2, followed by reflection across the x-axis, then translated

1 unit left and 3 units up

c.

∵ q(x) = x²

∵ n(x) = -(x - 7)² - 2

∴ m = -1 , h = 7 , k = -2

∵ m = -1

∴ q(x) is reflected across the x-axis

∵ h = 7

∴ q(x) is translated 7 units to the right

∵ k = -2

∴ q(x) is translated 2 units down

n(x) is the image of the parent function after reflection across the

x-axis, then translated 7 units right and 2 units down

Learn more:

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