Question

The graph of y=x is shifted 4 units up and 3 units right. Which equation represents the new graph?

O
y = -√-3+4
O
y=-√x+3+4
O
y=-x-4 + 3
y = -x + 4 + 3

Answer 1

`\textsf{A)} \quad y=-√(x-3)+4`

Explanation:

Translations

For
`a > 0`

`f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}`

`f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}`

`f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}`

`f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}`

Parent function (shown in blue on attached diagram):

`y=-√(x)`

Shifted 4 units up (shown in orange on attached diagram):

`\implies y=-√(x)+4`

Shifted 3 units right (shown in purple on attached diagram):

`\implies y=-√(x-3)+4`

Answer 2

y = -√(x - 3) + 4

Explanation:

On shifting 4 units up

• y = -√x + (4)
• y = -√x + 4

On shifting 3 units right

• y = -√(x - 3) + 4
• y = -√(x - 3) + 4
• Option 1