1. Given the linear parent function f(x)=x check all choices that describe the following transformation of the parent function g(x)=f(x)−6 A. Vertical shift up 6 units

B .Vertical shift down 6 units

C. Reflection across the x-axis

D. Vertical stretch by a factor of 6

E. Vertical compression by a factor of 6

The correct option is;

B. Vertical shift down 6 units

Step-by-step explanation:

The given parameters are;

The value of the function f(x) = x

The required transformation = g(x) = f(x) - 6

Whereby the slope, m, of the function f(x) = y = x, compared to the general equation of a straight line, y = m·x + c gives, m = 1, with the y-intercept at (0, 0), we have;

The values of the x and y coordinates of the function f(x) = x are equal, Therefore, a translation of g(x) = f(x) - 6, gives a function, g(x) = x - 6, whereby the slope, m = 1 as before, but the y-intercept is shifted down to -6 from 0, which is equivalent to a vertical shift down 6 units.

true statements:

a) x + y = y + x   ⇒ commutative property of addition

b) (x * y) * z = x * (y * z) ⇒ associative property of multiplication

d) (x + y) + z = x + (y + z) ⇒ associative property of addition

false statements:

c) x - y = y - x   should be: x - y = - y + x

e) (x - y) - z = x - (y - z) should be: (x - y) - z = x - (y + z)

step-by-step explanation:

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step-by-step explanation: