Question

1. the parent graph y = x was transformed. write a new equation to represent the transformations applied below to the mother function.

a. translation right 6 and down 2 \t\t\t\t\t\t\t y =

b. reflection over the x - axis and a scale change by 2 \t\t y =

c. scale change vertically by ½ and a translation right 8 \t y =

1. write the equation for the absolute value function graphed below:

Explanation:

Step1: Translate right 6, down 2

For parent $y=x$, right 6: $y=(x-6)$, down 2: $y=(x-6)-2 = x-8$

Step2: Reflect over x-axis, scale by 2

Reflect over x-axis: $y=-x$, scale by 2: $y=-2x$

Step3: Vertical scale ½, right 8

Vertical scale ½: $y=\frac{1}{2}x$, right 8: $y=\frac{1}{2}(x-8)$

Step4: Identify absolute value function

Parent $y=|x|$. Vertex at $(-3,-2)$, slope 1.
Shift left 3, down 2: $y=|x+3|-2$

Answer:

1. a. $y = x - 8$

b. $y = -2x$
c. $y = \frac{1}{2}(x-8)$

1. $y = |x+3| - 2$