If P(6,-9) is on the graph of f(x), find the corresponding point on the graph of y=3f(x-1)+10

Question

Please show work for, If P(6,-9) is on the graph of f(x), find the corresponding point on the graph of y=3f(x-1)+10.

Answer 1

Translate the point (6,-9) one unit to the right to get (7,-9).

Stretch (7,-9) vertically by a factor of 3 to obtain (7,-27).

Translating (7,-27) up 10 units, we arrive at the point (7,-17).

Answer 2

Given: f(x) is the parent function. It passes through the point P(6, -9).

y = 3f(x-1) + 10 means that this graph is shifted right by 1, vertically stretched by a factor of 3 and shifted up 10 from f(x).

Let x = 6 given from P(6, -9)

y = 3f(6-1) + 10

y = 3f(5) + 10

To actually find the value of "y" we would need to know f(5). We are only given f(6) = -9. Since we don't know what the parent function looks like, we can't calculate any further.

Answer: P(6, -9) --> (5, 3f(5) + 10)