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!

50.6

step-by-step explanation:

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be