The function transformations are:
Transformations involve translating, reflecting, rotating and dilating a function across the coordinate plane
The parent function of a quadratic function is represented as:
y = x^2
When the function is stretched horizontally by a factor of k, where k is between 0 and 1, we have:
y = (x/k)^2
Assume k = 1/4. we have:
y = (4x)^2
This means that the function (c) y = (4x)^2 is stretched horizontally by a factor of 1/4
When the function is stretched vertically by a factor of k, where k is greater than 1, we have:
y = k(x)^2
Assume k = 4. we have:
y = 4x^2
This means that the function (d) y = 4x^2 is stretched vertically by a factor of 4
Translating the function left is represented as:
y = (x + k)^2
Assume k = 2. we have:
y = (x + 2)^2
Reflecting the function across the x-axis is represented as
y = -(x + 2)^2
When the function is compressed vertically by a factor of k, where k is between 0 and 1, we have:
y = -k(x + 2)^2
Assume k = 1/2. we have:
y = -1/2(x + 2)^2
Translating the function up is represented as:
y = -1/2(x + 2)^2 + k
Assume k = 4. we have:
y = -1/2(x + 2)^2 + 4
Hence, the function (a) y = -1/2(x + 2)^2 + 4 is translated to the left by 2 units, reflected across the x-axis, compressed vertically by a factor of 1/2 and translated up by 4 units
Translating the function right is represented as:
y = (x - k)^2
Assume k = 1. we have:
y = (x - 1)^2
Reflecting the function across the x-axis is represented as
y = -(x - 1)^2
Translating the function down is represented as:
y = -(x - 1)^2 - k
Assume k = 2. we have:
y = -(x - 1)^2 - 2
Hence, the function (b) y = -(x - 1)^2 - 2 is translated right by 1 unit, reflected across the x-axis, and translated down by 2 units
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