The graph of f(x) = x has been translated left 2 units and up 1 unit. if no other transformations of the function have
occurred, which point lies on the new graph?
(4,2)
(-3,1)
(-2,5)
(-1,2)

The point (-1,2) lies on the new graph.

Step-by-step explanation:

The parent function is f(x) = x.

Now, if the graph of this above equation is translated by 2 units to the left, then the x-values of the parent function will reduce by 2 units for every corresponding value of y.

Therefore, the translated function will be f(x) - 2 = x

Again, the function so obtained is translated by 1 unit up, then the y-values of the function will increase by 1 unit for every corresponding value of x.

Therefore, the final transformed function will be f(x) - 2 = x + 1

⇒ f(x) = x + 3 (1)

Now, the only point (-1,2) satisfies the equation (1) from the given options.

Hence, the point (-1,2) lies on the new graph. (Answer)

parallel and congruent

step-by-step explanation:

the movement of translation is linear.   these have the same translation because you are using the same rule for each point of the triangle so you will see the same slope being used to get from a point on the triangle to its image.

same slope!   you should think parallel when you see those 2 word together (well unless it's the same line but it can't be because we are coming from different points here)

congruent! because each point is being moved the same distance.