Question

1) Determine the final transformed function that are applied to the originalfunction f(x) = (x]. Shift left 3 units, shift up 2 units, reflect about they-axisa) 1- x + 2 + 3 b) - x + 3 + 2c) |x - 3 + 2d) (x + 31 - 2 e) None of them2) If (3,6) is a point on the graph of y = f(x) which of the following pointsmust be on the graph of y = -f(x)a) (6-3) b) (-3,-6) c)(-6,-3) d) (3,-6)d) None of the above

Answer 1

1.

Original function

`f(x)=|x|`

Left 3 units. Horizontal move is applied directly to the variable

`|x+3|`

Up 2 units. Vertical move is applied to whole function

`|x+3|+2`

reflect obout the y-axis, we change the sign of the variable, then

`f(x)=|-x+3|+2`

then right option is B

2.

`y=f(x)`

then -f(x) is -y

`-y=-f(x)`

then change the value of -y

So the point must be on the graph of -f(x) is

`(3,-6)`

Then right option is D