Question

Rewrite y =
`\sqrt9{x} +45` – 2 to make it easy to graph using a translation. Describe the graph.

Rewritten, y =
`√(x)-5` – 2. It is the graph of y =
`√(x)` translated 5 units left and 2 units down.

Rewritten, y =
`√(x) +5` – 2. It is the graph of y =
`√(x)` translated 5 units right and 2 units down.

Rewritten, y =
`\sqrt[3]{x} +5` – 2. It is the graph of y =
`\sqrt[3]{x}` translated 5 units left and 2 units down.

Rewritten, y =
`\sqrt[3]{x} +5`– 2. It is the graph of y =
`\sqrt[3]{x}`translated 5 units right and 2 units down.

Answer 1

(1) We have been given a function:
`y=√(9x)+45-2`

We can rewrite it using translation is:

It is the graph of
`y=√(9x)` translated 45 units left and 2 units down.

(2) Now,
`y=√(x)-5-2`

So this is the graph of
`y=√(x)` translated 5 units right and 2 units down.

(3)
`y=√(x)+5-2`

So, this is the graph of
`y=√(x)` translated 5 units left and 2 units down.

(4)
`y=\sqrt[3]{x}+5-2`

It is the graph of
`y=\sqrt[3]{x}`

translated 5 units left and 2 units down.

(5)
`y=\sqrt[3]{x}+5-2`

It is the graph of
`y=\sqrt[3]{x}`

translated 5 units left and 2 units down.