Question

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)

Answer 1

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?

the answer to this question is: ( –1, 2)

Answer 2

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

Explanation:

The parent function is f(x) = |x|.

When we translate this function left by units then we will have to add 2 to x. Hence, we have

f(x) = |x+2|

Now, the graph is shifted 1 unit up. Hence, add 1 to the function

f(x) = |x+2| + 1

This is the equation for new graph. Now, we substitute all the given points and check which point satisfies this equation.

For the point (-4,2)

2 = |-4 + 2| +1

2=3 (False)

For the point (-3,1)

1= |-3 + 2| +1

1=2 (False)

For the point (-2,5)

5= |-2 + 2| +1

5=1 (False)

For the point (-1,2)

2= |-1+ 2| +1

2=2 (True)

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