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
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