Write the expressions for when you translate the graph of y = x+2 a) one unit up, b) one unit down, c) one unit to the left, d) one unit to the right.

Answers and Step-by-step explanations:

Vertical transformations affect the entire function, while horizontal transformations influence only the x - only the x is altered. Vertical transformations include vertical stretches and shrinks, reflections over the x axis, and translations up and/or down. Horizontal transformations are horizontal stretches and shrinks, reflections over the y axis, and translations left and/or right.

a) "translate one unit up"; since we're translating up, we know this is a vertical translation, which will affect the entire function. So, the function will go from y = x + 2 to y = (x + 2) + 1 or y = x + 3.

b) "translate one unit down"; again, since we're translating down, we know this is another vertical translation, which will affect the entire function. So, our function goes from y = x + 2 to y = (x + 2) - 1 or y = x + 1.

c) "translate one unit to the left"; since we're translating to the left, we know that this will be a horizontal transformation, which will only affect the x. So our function goes from y = x + 2 to y = (x + 1) + 2 or y = x + 3. (Note that "left" will use a "+" sign because horizontal transformations are weird and "backward")

d) "translate one unit to the right"; again, since we're moving to the right, we know this is another horizontal transformation, which will only affect the x. So our function goes from y = x + 2 to y = (x - 1) + 2 or y = x + 1. (Again note that "right" uses "-" instead of "+" as we would think because horizontal transformations are weirdly "backward").

Hope this helps!

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)